Edgar Filing: FIRST TRUST ENERGY INFRASTRUCTURE FUND

UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

FORM N-Q

QUARTERLY SCHEDULE OF PORTFOLIO HOLDINGS OF REGISTERED MANAGEMENT
INVESTMENT COMPANY

Investment Company Act file number 811-22528
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First Trust Energy Infrastructure Fund
---------------------------------------------------------------
(Exact name of registrant as specified in charter)

120 East Liberty Drive, Suite 400
Wheaton, IL 60187
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(Address of principal executive offices) (Zip code)

W. Scott Jardine, Esq.
First Trust Portfolios L.P.
120 East Liberty Drive, Suite 400
Wheaton, IL 60187
---------------------------------------------------------------
(Name and address of agent for service)

Registrant's telephone number, including area code: 630-765-8000

Date of fiscal year end: November 30
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Date of reporting period: August 31, 2012
-----------------

Form N-Q is to be used by management investment companies, other than small
business investment companies registered on Form N-5 (ss.ss. 239.24 and 274.5 of
this chapter), to file reports with the Commission, not later than 60 days after
the close of the first and third fiscal quarters, pursuant to rule 30b1-5 under
the Investment Company Act of 1940 (17 CFR 270.30b1-5). The Commission may use
the information provided on Form N-Q in its regulatory, disclosure review,
inspection, and policymaking roles.

A registrant is required to disclose the information specified by Form N-Q, and
the Commission will make this information public. A registrant is not required
to respond to the collection of information contained in Form N-Q unless the
Form displays a currently valid Office of Management and Budget ("OMB") control
number. Please direct comments concerning the accuracy of the information
collection burden estimate and any suggestions for reducing the burden to the
Secretary, Securities and Exchange Commission, 100 F Street, NE, Washington, DC
20549. The OMB has reviewed this collection of information under the clearance
requirements of 44 U.S.C. ss. 3507.

ITEM 1. SCHEDULE OF INVESTMENTS. The Schedule(s) of Investments is attached
herewith.

FIRST TRUST ENERGY INFRASTRUCTURE FUND
PORTFOLIO OF INVESTMENTS
AUGUST 31, 2012 (UNAUDITED)

SHARES/
UNITS DESCRIPTION VALUE
--------------- -------------------------------------------------------------------- --------------
COMMON STOCKS - 96.5%

ELECTRIC UTILITIES - 25.5%

243,266 Duke Energy Corp. (a)............................................... $ 15,758,771
284,600 Emera, Inc. (CAD) (a)............................................... 9,937,542
366,450 Exelon Corp. (a).................................................... 13,364,432
109,800 Fortis, Inc. (CAD) (a).............................................. 3,618,972
105,000 ITC Holdings Corp. (a).............................................. 7,557,900
272,900 NextEra Energy, Inc. (a)............................................ 18,368,899
365,800 Northeast Utilities (a)............................................. 13,779,686
464,500 Southern Co. (a).................................................... 21,055,785
--------------
103,441,987
--------------

GAS UTILITIES - 5.5%
31,600 ONEOK, Inc. ........................................................ 1,407,148
323,400 Questar Corp. (a)................................................... 6,387,150
473,979 UGI Corp. (a)....................................................... 14,446,880
--------------
22,241,178
--------------

MULTI-UTILITIES - 20.4%
35,000 Atco, Ltd. (CAD) (a)................................................ 2,712,655
45,500 Canadian Utilities, Ltd. (CAD) (a).................................. 3,137,804
797,600 Centerpoint Energy, Inc. (a)........................................ 16,263,064
421,400 Dominion Resources, Inc. (a)........................................ 22,115,072
185,000 National Grid PLC, ADR (a).......................................... 10,076,950
745,400 NiSource, Inc. (a).................................................. 18,143,036
75,000 Sempra Energy (a)................................................... 4,965,000
135,000 Wisconsin Energy Corp. (a).......................................... 5,124,600
--------------
82,538,181
--------------

OIL, GAS & CONSUMABLE FUELS - 45.1%
1,177,183 Enbridge Energy Management, LLC (a) (b)............................. 36,645,707
474,600 Enbridge Income Fund Holdings, Inc. (CAD) (a)....................... 10,794,352
326,869 Enbridge, Inc. (a).................................................. 12,885,176
182,300 Keyera Corp. (CAD) (a).............................................. 8,322,090
491,736 Kinder Morgan Management, LLC (a) (b)............................... 36,447,479
326,500 Kinder Morgan, Inc. ................................................ 11,678,905
482,100 Pembina Pipeline Corp. (CAD) (a).................................... 13,067,930
540,950 Spectra Energy Corp. (a)............................................ 15,287,247
360,400 TransCanada Corp. (a)............................................... 16,243,228
258,000 Veresen, Inc. (CAD) (a)............................................. 3,420,806
560,700 Williams Cos., Inc. (a)............................................. 18,093,789
--------------
182,886,709
--------------
TOTAL COMMON STOCKS ................................................ 391,108,055
(Cost $356,395,268) --------------

MASTER LIMITED PARTNERSHIPS - 31.1%

GAS UTILITIES - 1.7%
152,764 AmeriGas Partners, L.P. (a)......................................... 6,541,354
10,700 Suburban Propane Partners, L.P. .................................... 414,090
--------------
6,955,444
--------------

See Notes to Quarterly Portfolio of Investments Page 1

FIRST TRUST ENERGY INFRASTRUCTURE FUND
PORTFOLIO OF INVESTMENTS - (CONTINUED)
AUGUST 31, 2012 (UNAUDITED)

SHARES/
UNITS DESCRIPTION VALUE
--------------- -------------------------------------------------------------------- --------------
MASTER LIMITED PARTNERSHIPS - (CONTINUED)

OIL, GAS & CONSUMABLE FUELS - 29.4%

20,000 Alliance GP Holdings, L.P. ......................................... $ 968,000
79,565 Alliance Resource Partners, L.P. (a)................................ 4,927,460
155,460 Buckeye Partners, L.P. (a).......................................... 7,682,833
162,000 El Paso Pipeline Partners, L.P. (a)................................. 5,862,780
149,000 Energy Transfer Equity, L.P. (a).................................... 6,548,550
41,600 Enterprise Products Partners, L.P. (a).............................. 2,221,440
131,223 Holly Energy Partners, L.P. (a)..................................... 8,837,869
64,300 Magellan Midstream Partners, L.P. (a)............................... 5,334,971
173,239 Natural Resource Partners, L.P. (a)................................. 3,586,047
219,000 NuStar Energy, L.P. (a)............................................. 11,107,680
29,600 NuStar GP Holdings, LLC ............................................ 901,912
16,000 ONEOK Partners, L.P. ............................................... 909,120
124,443 Plains All American Pipeline, L.P. (a).............................. 10,768,053
117,700 Spectra Energy Partners, L.P. (a)................................... 3,768,754
154,350 Sunoco Logistics Partners, L.P. (a)................................. 7,200,428
303,095 TC Pipelines, L.P. (a).............................................. 13,766,575
304,828 Teekay LNG Partners, L.P. (a)....................................... 12,107,768
246,570 TransMontaigne Partners, L.P. (a)................................... 9,009,668
66,300 Williams Partners, L.P. (a)......................................... 3,419,754
--------------
118,929,662
--------------
TOTAL MASTER LIMITED PARTNERSHIPS .................................. 125,885,106
(Cost $109,794,998) --------------

TOTAL INVESTMENTS - 127.6% ......................................... 516,993,161
(Cost $466,190,266) (c) --------------

NUMBER OF
CONTRACTS DESCRIPTION VALUE
--------------- -------------------------------------------------------------------- --------------
CALL OPTIONS WRITTEN - (0.4%)
Centerpoint Energy, Inc. Calls
1,500 @ 22.5 due November 12 ............................................. (18,750)
1,400 @ 22.5 due February 13 ............................................. (45,500)
(64,250)

Dominion Resources, Inc. Calls
1,500 @ 55 due September 12 .............................................. (7,500)
1,800 @ 57.5 due January 13 .............................................. (36,000)
--------------
(43,500)
--------------
Duke Energy Corp. Calls
800 @ 70 due September 12 .............................................. (4,000)
400 @ 24 due October 12 (d)............................................. (2,000)
100 @ 70 due October 12 ................................................ (500)
800 @ 23 due October 12 (d)............................................. (6,000)
600 @ 70 due January 13 ................................................ (24,600)
--------------
(37,100)
--------------

Page 2 See Notes to Quarterly Portfolio of Investments

FIRST TRUST ENERGY INFRASTRUCTURE FUND
PORTFOLIO OF INVESTMENTS - (CONTINUED)
AUGUST 31, 2012 (UNAUDITED)

1,700 @ 45 due October 12 ................................................ $ (25,500)
--------------
Exelon Corp. Calls
600 @ 39 due October 12 ................................................ (6,000)
1,500 @ 40 due October 12 ................................................ (7,500)
210 @ 42 due October 12 ................................................ (1,050)
--------------
(14,550)
--------------
Kinder Morgan, Inc. Calls
1,542 @ 35 due September 12 .............................................. (131,070)
800 @ 40 due September 12 .............................................. (1,600)
300 @ 37.5 due September 12 ............................................ (1,800)
400 @ 35 due December 12 ............................................... (74,800)
200 @ 37.5 due January 13 .............................................. (19,200)
--------------
(228,470)
--------------
National Grid PLC Calls
1,050 @ 55 due September 12 .............................................. (39,375)
100 @ 55 due December 12 ............................................... (13,000)
--------------
(52,375)
--------------
NextEra Energy, Inc. Calls
100 @ 67.5 due September 12 ............................................ (7,000)
270 @ 70 due September 12 .............................................. (1,350)
15 @ 65 due September 12 .............................................. (3,900)
500 @ 70 due October 12 ................................................ (12,500)
500 @ 72.5 due December 12 ............................................. (10,000)
--------------
(34,750)
--------------
NiSource, Inc. Call
700 @ 25 due September 12 .............................................. (8,750)
--------------
Northeast Utilities Call
900 @ 40 due October 12 ................................................ (36,000)
--------------
ONEOK, Inc. Call
300 @ 45 due October 12 ................................................ (30,000)
--------------
Questar Corp. Calls
750 @ 21 due October 12 ................................................ (7,500)
500 @ 21 due January 13 ................................................ (18,750)
547 @ 22 due January 13 ................................................ (6,838)
--------------
(33,088)
--------------
Southern Co. Calls
600 @ 48 due November 12 ............................................... (6,600)
800 @ 50 due January 13 ................................................ (5,600)
--------------
(12,200)
--------------
Spectra Energy Corp. Calls
786 @ 29 due September 12 .............................................. (11,790)
2,300 @ 30 due September 12 .............................................. (11,500)
500 @ 31 due September 12 .............................................. (2,500)

See Notes to Quarterly Portfolio of Investments Psge 3

FIRST TRUST ENERGY INFRASTRUCTURE FUND
PORTFOLIO OF INVESTMENTS - (CONTINUED)
AUGUST 31, 2012 (UNAUDITED)

200 @ 33 due September 12 .............................................. $ (1,000)
800 @ 31 due December 12 ............................................... (16,000)
--------------
(42,790)
--------------
TransCanada Corp. Call
1,600 @ 45 due November 12 ............................................... (192,000)
--------------
UGI Corp. Call
1,575 @ 30 due October 12 ................................................ (212,625)
--------------
Williams Cos., Inc. Calls
1,800 @ 33 due September 12 .............................................. (84,600)
800 @ 35 due November 12 ............................................... (54,400)
1,500 @ 34 due November 12 ............................................... (144,000)
400 @ 33 due November 12 ............................................... (53,600)
--------------
(336,600)
--------------
TOTAL CALL OPTIONS WRITTEN ......................................... (1,404,548)
(Premiums received $1,606,116) --------------

OUTSTANDING LOAN - (31.6%) ......................................... (128,000,000)

NET OTHER ASSETS AND LIABILITIES - 4.4% ............................ 17,666,278
--------------
NET ASSETS - 100.0% ................................................ $ 405,254,891
==============

---------------------------------------

(a) All or a portion of this security is available to serve as collateral on
the outstanding loan.

(b) Non-income producing security which pays in-kind distributions.

(c) Aggregate cost for financial reporting purposes, which approximates the
aggregate cost for federal income tax purposes. As of August 31, 2012, the
aggregate gross unrealized appreciation for all securities in which there
was an excess of value over tax cost was $55,407,900 and the aggregate
gross unrealized depreciation for all securities in which there was an
excess of tax cost over value was $4,605,005.

(d) Duke Energy Corp. (DUK) announced a 1 for 3 reverse stock split that
became effective on July 2, 2012. On this date, each DUK share was
converted into the right to receive 0.333333 (new) Duke Energy Corp common
shares and the ticker symbols associated with the Duke Energy Corp. call
options held by the Fund changed from DUK to DUK1. The contract size of
each outstanding Duke Energy Corp. call option held in the Fund prior to
July 2, 2012 changed from 100 to 33. This call option contract was entered
into prior to July 2, 2012, the effective date of the 1 for 3 reverse
stock split.

ADR American Depositary Receipt

CAD Canadian Dollar - security is denominated in Canadian Dollars and is
translated into U.S. Dollars based upon the current exchange rate.

Page 4 See Notes to Quarterly Portfolio of Investments

FIRST TRUST ENERGY INFRASTRUCTURE FUND
PORTFOLIO OF INVESTMENTS - (CONTINUED)
AUGUST 31, 2012 (UNAUDITED)

VALUATION INPUTS

A summary of the inputs used to value the Fund's investments as of August 31,
2012 is as follows (see Note A - Portfolio Valuation in the Notes to Quarterly
Portfolio of Investments):

ASSETS TABLE
LEVEL 2 LEVEL 3
TOTAL LEVEL 1 SIGNIFICANT SIGNIFICANT
VALUE AT QUOTED OBSERVABLE UNOBSERVABLE
8/31/2012 PRICES INPUTS INPUTS
-------------- -------------- -------------- --------------

Common Stocks*................................. $ 391,108,055 $ 391,108,055 $ -- $ --
Master Limited Partnerships*................... 125,885,106 125,885,106 -- --
-------------- -------------- -------------- --------------
TOTAL INVESTMENTS.............................. $ 516,993,161 $ 516,993,161 $ -- $ --
============== ============== ============== ==============

LIABILITIES TABLE
LEVEL 2 LEVEL 3
TOTAL LEVEL 1 SIGNIFICANT SIGNIFICANT
VALUE AT QUOTED OBSERVABLE UNOBSERVABLE
8/31/2012 PRICES INPUTS INPUTS
-------------- -------------- -------------- --------------
Call Options Written........................... $ (1,404,548) $ (1,404,548) $ -- $ --
============== ============== ============== ==============

* See Portfolio of Investments for industry breakout.

All transfers in and out of the Levels during the period are assumed to be
transferred on the last day of the period at their current value. As of August
31, 2012, the Fund transferred common stock valued at $26,793,093 from Level 2
to Level 1 of the fair value hierarchy. The common stock that transferred from
Level 2 to Level 1 did so as a result of the availability of quoted prices that
were not previously available in an active market. This common stock was
previously fair valued in accordance with procedures adopted by the Fund's Board
of Trustees and the provisions of the Investment Company Act of 1940, as
amended.

See Notes to Quarterly Portfolio of Investments Page 5

NOTES TO QUARTERLY PORTFOLIO OF INVESTMENTS

FIRST TRUST ENERGY INFRASTRUCTURE FUND
AUGUST 31, 2012 (UNAUDITED)

1. VALUATION AND INVESTMENT PRACTICES

A. PORTFOLIO VALUATION:

The net asset value ("NAV") of the Common Shares of First Trust Energy
Infrastructure Fund (the "Fund") is determined daily as of the close of regular
trading on the New York Stock Exchange ("NYSE"), normally 4:00 p.m. Eastern
time, on each day the NYSE is open for trading. If the NYSE closes early on a
valuation day, the NAV is determined as of that time. Domestic debt securities
and foreign securities are priced using data reflecting the earlier closing of
the principal markets for those securities. The NAV per Common Share is
calculated by dividing the value of all assets of the Fund (including accrued
interest and dividends), less all liabilities (including accrued expenses,
dividends declared but unpaid and any borrowings of the Fund) by the total
number of Common Shares outstanding.

The Fund's investments are valued daily in accordance with valuation procedures
adopted by the Fund's Board of Trustees, and in accordance with provisions of
the Investment Company Act of 1940 , as amended (the "1940 Act"). The following
securities, for which accurate and reliable market quotations are readily
available, will be valued as follows:

Common stocks, master limited partnerships ("MLPs") and other securities
listed on any national or foreign exchange (excluding the NASDAQ National
Market ("NASDAQ") and the London Stock Exchange Alternative Investment
Market ("AIM")) are valued at the last sale price on the exchange on which
they are principally traded. If there are no transactions on the valuation
day, the securities are valued at the mean between the most recent bid and
asked prices.

Securities listed on the NASDAQ or the AIM are valued at the official
closing price. If there is no official closing price on the valuation day,
the securities are valued at the mean between the most recent bid and
asked prices.

Securities traded in the over-the-counter market are valued at their
closing bid prices.

Exchange-traded options and futures contracts are valued at the closing
price in the market where such contracts are principally traded. If no
closing price is available, exchange-traded options and futures contracts
are valued at the mean between the most recent bid and asked prices.
Over-the-counter options and futures contracts are valued at their closing
bid prices.

Short-term investments that mature in less than 60 days when purchased are
valued at amortized cost.

All market quotations used in valuing the Fund's securities will be obtained
from a third party pricing service. If no quotation is received from a pricing
service, attempts will be made to obtain one or more broker quotes for the
security. In the event the pricing service does not provide a valuation, broker
quotations are not readily available, or the valuations received are deemed
unreliable, the Fund's Board of Trustees has designated First Trust Advisors
L.P. ("First Trust") to use a fair value method to value the Fund's securities.
Additionally, if events occur after the close of the principal markets for
certain securities (e.g., domestic debt and foreign securities) that could
materially affect the Fund's NAV, First Trust will use a fair value method to
value the Fund's securities. The use of fair value pricing is governed by
valuation procedures adopted by the Fund's Board of Trustees, and in accordance
with the provisions of the 1940 Act. As a general principle, the fair value of a
security is the amount which the Fund might reasonably expect to receive for the
security upon its current sale. However, in light of the judgment involved in
fair valuations, there can be no assurance that a fair value assigned to a
particular security will be the amount which the Fund might be able to receive
upon its current sale. Fair valuation of a security will be based on the
consideration of all available information, including, but not limited to the
following:

1) the type of security;

2) the size of the holding;

3) the initial cost of the security;

4) transactions in comparable securities;

5) price quotes from dealers and/or pricing services;

6) relationships among various securities;

7) information obtained by contacting the issuer, analysts, or the
appropriate stock exchange;

8) an analysis of the issuer's financial statements; and

9) the existence of merger proposals or tender offers that might affect
the value of the security.

If the securities in question are foreign securities, the following additional
information may be considered:

1) the value of similar foreign securities traded on other foreign
markets;

2) ADR trading of similar securities;

3) closed-end fund trading of similar securities;

4) foreign currency exchange activity;

5) the trading prices of financial products that are tied to baskets of
foreign securities;

6) factors relating to the event that precipitated the pricing problem;

7) whether the event is likely to recur; and

8) whether the effects of the event are isolated or whether they affect
entire markets, countries or regions.

Page 6

NOTES TO FINANCIAL STATEMENTS - (CONTINUED)

FIRST TRUST ENERGY INFRASTRUCTURE FUND
AUGUST 31, 2012 (UNAUDITED)

The Fund is subject to fair value accounting standards that define fair value,
establish the framework for measuring fair value and provide a three-level
hierarchy for fair valuation based upon the inputs to the valuation as of the
measurement date. The three levels of the fair value hierarchy are as follows:

o Level 1 - Level 1 inputs are quoted prices in active markets for
identical investments. An active market is a market in which
transactions for the investment occur with sufficient frequency and
volume to provide pricing information on an ongoing basis.

o Level 2 - Level 2 inputs are observable inputs, either directly or
indirectly, and include the following:

o Quoted prices for similar investments in active markets.

o Quoted prices for identical or similar investments in markets
that are non-active. A non-active market is a market where
there are few transactions for the investment, the prices are
not current, or price quotations vary substantially either
over time or among market makers, or in which little
information is released publicly.

o Inputs other than quoted prices that are observable for the
investment (for example, interest rates and yield curves
observable at commonly quoted intervals, volatilities,
prepayment speeds, loss severities, credit risks, and default
rates).

o Inputs that are derived principally from or corroborated by
observable market data by correlation or other means.

o Level 3 - Level 3 inputs are unobservable inputs. Unobservable
inputs may reflect the reporting entity's own assumptions about the
assumptions that market participants would use in pricing the
investment.

The inputs or methodology used for valuing investments are not necessarily an
indication of the risk associated with investing in those investments. A summary
of the inputs used to value the Fund's investments as of August 31, 2012, is
included with the Fund's Portfolio of Investments.

B. OPTION CONTRACTS:

The Fund is subject to equity price risk in the normal course of pursuing its
investment objective and may enter into options written to hedge against changes
in the value of equities. Also, by writing (selling) options, the Fund seeks to
generate additional income, in the form of premiums received for writing
(selling) the options. The Fund may write (sell) covered call or put options
("options") on all or a portion of the common stock of energy companies held in
the Fund's portfolio as determined to be appropriate by Energy Income Partners,
LLC ("EIP" or the "Sub-Advisor"). The number of options the Fund can write
(sell) is limited by the amount of common stock of energy companies the Fund
holds in its portfolio. The Fund will not write (sell) "naked" or uncovered
options. Options are marked-to-market daily and their value will be affected by
changes in the value and dividend rates of the underlying equity securities,
changes in interest rates, changes in the actual or perceived volatility of the
securities markets and the underlying equity securities and the remaining time
to the options' expiration. The value of options may also be adversely affected
if the market for the options becomes less liquid or trading volume diminishes.

Options the Fund writes (sells) will either be exercised, expire or be cancelled
pursuant to a closing transaction. If the price of the underlying equity
security exceeds the option's exercise price, it is likely that the option
holder will exercise the option. If an option written (sold) by the Fund is
exercised, the Fund would be obligated to deliver the underlying equity security
to the option holder upon payment of the strike price. In this case, the option
premium received by the Fund will be added to the amount realized on the sale of
the underlying security for purposes of determining gain or loss. If the price
of the underlying equity security is less than the option's strike price, the
option will likely expire without being exercised. The option premium received
by the Fund will, in this case, be treated as short-term capital gain on the
expiration date of the option. The Fund may also elect to close out its position
in an option prior to its expiration by purchasing an option of the same series
as the option written (sold) by the Fund.

The options that the Fund writes (sells) give the option holder the right, but
not the obligation, to purchase a security from the Fund at the strike price on
or prior to the option's expiration date. The ability to successfully implement
the writing (selling) of covered call options depends on the ability of the
Sub-Advisor to predict pertinent market movements, which cannot be assured.
Thus, the use of options may require the Fund to sell portfolio securities at
inopportune times or for prices other than current market value, which may limit
the amount of appreciation the Fund can realize on an investment, or may cause
the Fund to hold a security that it might otherwise sell. As the writer (seller)
of a covered option, the Fund foregoes, during the option's life, the
opportunity to profit from increases in the market value of the security
covering the option above the sum of the premium and the strike price of the
option, but has retained the risk of loss should the price of the underlying
security decline. The writer (seller) of an option has no control over the time
when it may be required to fulfill its obligation as a writer (seller) of the
option. Once an option writer (seller) has received an exercise notice, it
cannot effect a closing purchase transaction in order to terminate its
obligation under the option and must deliver the underlying security to the
option holder at the exercise price.

Page 7

NOTES TO FINANCIAL STATEMENTS - (CONTINUED)

FIRST TRUST ENERGY INFRASTRUCTURE FUND
AUGUST 31, 2012 (UNAUDITED)

Over-the-counter ("OTC") options have the risk of the potential inability of
counterparties to meet the terms of their contracts. The Fund's maximum equity
price risk for purchased options is limited to the premium initially paid. In
addition, certain risks may arise upon entering into option contracts including
the risk that an illiquid secondary market will limit the Fund's ability to
close out an option contract prior to the expiration date and that a change in
the value of the option contract may not correlate exactly with changes in the
value of the securities hedged.

C. SECURITIES TRANSACTIONS:

Securities transactions are recorded as of the trade date. Realized gains and
losses from securities transactions are recorded on the identified cost basis.

Distributions received from the Fund's investments in MLPs generally are
comprised of return of capital and investment income. The Fund records estimated
return of capital and investment income based on historical information
available from each MLP. These estimates may subsequently be revised based on
information received from the MLPs after their tax reporting periods are
concluded.

D. FOREIGN CURRENCY:

The books and records of the Fund are maintained in U.S. dollars. Foreign
currencies, investments and other assets and liabilities are translated into
U.S. dollars at the exchange rates prevailing at the end of the period.
Purchases and sales of investments and items of income and expense are
translated on the respective dates of such transactions.

E. RESTRICTED SECURITIES:

The Fund may invest up to 15% of its Managed Assets in restricted securities.
Managed Assets means the total asset value of the Fund minus the sum of the
Fund's liabilities other than the principal amount of borrowings. Restricted
securities are securities that may not be offered for public sale without first
being registered under the Securities Act of 1933, as amended (the "1933 Act").
Prior to registration, restricted securities may only be resold in transactions
exempt from registration under Rule 144A under the 1933 Act, normally to
qualified institutional buyers. As of August 31, 2012, the Fund held no
restricted securities.

2. OPTION ACTIVITY

Written option activity for the Fund for the period ended August 31, 2012 was as
follows:

Number
of
Written Options Contracts Premiums
--------------------------------------------- ---------- -----------
Options outstanding at November 30, 2011..... 29,526 $ 1,735,315
Options Written.............................. 97,259 3,619,993
Options Expired.............................. (58,309) (2,285,068)
Options Exercised............................ (27,817) (1,161,089)
Options Closed............................... (4,614) (303,035)
---------- -----------
Options outstanding at August 31, 2012....... 36,045 $ 1,606,116
========== ===========

Page 8

ITEM 2. CONTROLS AND PROCEDURES.

(a) The registrant's principal executive and principal financial officers, or
persons performing similar functions, have concluded that the
registrant's disclosure controls and procedures (as defined in Rule
30a-3(c) under the Investment Company Act of 1940, as amended (the "1940
Act") (17 CFR 270.30a-3(c))) are effective, as of a date within 90 days
of the filing date of the report that includes the disclosure required by
this paragraph, based on their evaluation of these controls and
procedures required by Rule 30a-3(b) under the 1940 Act (17 CFR
270.30a-3(b)) and Rules 13a-15(b) or 15d-15(b) under the Securities
Exchange Act of 1934, as amended (17 CFR 240.13a-15(b) or 240.15d-15(b)).

(b) There were no changes in the registrant's internal control over financial
reporting (as defined in Rule 30a-3(d) under the 1940 Act (17 CFR
270.30a-3(d)) that occurred during the registrant's last fiscal quarter
that have materially affected, or are reasonably likely to materially
affect, the registrant's internal control over financial reporting.

ITEM 3. EXHIBITS.

Certifications pursuant to Rule 30a-2(a) under the 1940 Act and Section 302 of
the Sarbanes-Oxley Act of 2002 are attached hereto.

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, the registrant has duly caused this report to be
signed on its behalf by the undersigned, thereunto duly authorized.

(Registrant) First Trust Energy Infrastructure Fund
----------------------------------------------

By (Signature and Title)* /s/ Mark R. Bradley
------------------------------------------------------
Mark R. Bradley
President and Chief Executive Officer
(principal executive officer)

Date October 23, 2012
----------------------

Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, this report has been signed below by the
following persons on behalf of the registrant and in the capacities and on the
dates indicated.

By (Signature and Title)* /s/ Mark R. Bradley
------------------------------------------------------
Mark R. Bradley
President and Chief Executive Officer
(principal executive officer)

Date October 23, 2012
----------------------

By (Signature and Title)* /s/ James M. Dykas
------------------------------------------------------
James M. Dykas
Chief Financial Officer and Chief Accounting Officer
(principal financial officer)

Date October 23, 2012
----------------------

*Print the name and title of each signing officer under his or her signature.