As filed with the Securities and Exchange Commission on October  28, 2004

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 811-21462

Tortoise Energy Infrastructure Corporation

(Exact name of registrant as specified in charter)

10801 Mastin Blvd., Suite 222, Overland Park, KS 66210

(Address of principal executive offices) (Zip code)

David J. Schulte, 10801 Mastin Blvd., Suite 222, Overland Park, KS 66210

(Name and address of agent for service)

913-981-1020

Registrant's telephone number, including area code

Date of fiscal year end: November 30

Date of reporting period: August 31, 2004

Item 1. Schedule of Investments.

Tortoise Energy Infrastructure Corporation
Schedule of Investments (Unaudited)		August 31, 2004
MASTER LIMITED PARTNERSHIPS - 131.20%	Shares	Value
Coal - 3.29%
Natural Resource Partners L.P.	253,700	$ 10,135,315
Crude/Refined Products Pipelines - 82.23%
Enbridge Energy Partners, L.P.	357,300	17,368,353
Holly Energy Partners, L.P.*	427,070	12,299,616
Kaneb Pipe Line Partners, L.P.	388,500	19,230,750
Kinder Morgan Energy Partners, L.P.	118,400	5,271,168
Kinder Morgan Management, LLC #	804,467	31,269,632
K-Sea Transportation Partners L.P.	65,600	1,880,752
Magellan Midstream Partners, L.P.	796,217	41,642,149
Pacific Energy Partners, L.P.	565,800	16,006,482
Plains All American Pipeline, L.P.	728,335	24,260,839
Plains All American Pipeline, L.P. - Unregistered ^	486,855	15,243,430
Sunoco Logistics Partners L.P.	838,200	32,279,082
TEPPCO Partners, L.P.	538,500	21,480,765
Valero L.P.	287,100	15,316,785
		253,549,803
Natural Gas/NGL Pipelines - 13.19%
Enterprise Products Partners L.P.	1,092,200	24,345,138
GulfTerra Energy Partners, L.P.	406,995	16,344,919
		40,690,057
Natural Gas Gathering/Processing - 22.14%
Energy Transfer Partners, L.P.	907,244	39,356,245
Markwest Energy Partners, L.P.	126,100	5,550,922
Markwest Energy Partners, L.P. - Unregistered ^	579,710	23,350,719
		68,257,886
Propane Distribution - 10.35%
Inergy, L.P.	1,300,000	31,928,000
TOTAL MASTER LIMITED PARTNERSHIPS (Cost $379,862,712)		404,561,061
	Principal
PROMISSORY NOTES - 2.60%	Amount
K-Sea Transportation Partners L.P. - Unregistered, 8.000%, Due 03/31/2009
(Cost $8,021,504) ^ @	$ 8,137,500	8,021,504
INVESTMENT COMPANIES - 6.95%	Shares
First American Prime Obligations Fund - Class Z	10,709,914	10,709,914
First American Treasury Obligations Fund - Class Z	10,709,914	10,709,914
(Cost $21,419,828)		21,419,828
TOTAL INVESTMENTS - 140.75% (Cost $409,304,044)		434,002,393
INTEREST RATE SWAP CONTRACTS - (0.48%)
$60,000,000 notional, Due 7/10/2007 - Unrealized Depreciation		(811,992)
$50,000,000 notional, Due 7/17/2007 - Unrealized Depreciation		(673,195)
		(1,485,187)
LIABILITIES IN EXCESS OF OTHER ASSETS - (40.27%)		(124,169,925)
TOTAL NET ASSETS APPLICABLE TO COMMON SHAREHOLDERS - 100.00%		$ 308,347,281
Footnotes and Abbreviations
* Non-Income producing security.
^ Fair valued securities represent a total market value of $46,615,653 which represents 15.12% of net assets.
# Security distributions are paid in kind.
@ Security is a variable rate instrument. Interest rate is as of August 31, 2004.

Item 2. Controls and Procedures.

(a)   The Registrant’s President/Chief Executive Officer and Treasurer/Chief Financial Officer have concluded that the Registrant's disclosure controls and procedures (as defined in Rule 30a-3(c) under the Investment Company Act of 1940 (the "1940 Act")) 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 the evaluation of these controls and procedures required by Rule 30a-3(b) under the 1940 Act and Rules 15d-15(b) under the Securities Exchange Act of 1934, as amended.

(b)   There were no changes in the Registrant's internal control over financial reporting (as defined in Rule 30a-3(d) under the Act) that occurred during the Registrant's last fiscal half-year that has materially affected, or is reasonably likely to materially affect, the Registrant's internal control over financial reporting.

Item 3. Exhibits.

Separate certifications for each principal executive officer and principal financial officer of the registrant as required by Rule 30a-2(a) under the Act (17 CFR 270.30a-2(a)). Filed herewith.

CERTIFICATION

I, David J. Schulte, certify that:

1.   I have reviewed this report on Form N-Q of Tortoise Energy Infrastructure Corporation;

2.   Based on my knowledge, this report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by this report;

3.   Based on my knowledge, the schedules of investments included in this report fairly present in all material respects the investments of the registrant as of the end of the fiscal quarter for which the report is filed;

4.   The registrant's other certifying officer(s) and I are responsible for establishing and maintaining disclosure controls and procedures (as defined in Rule 30a-3(c) under the Investment Company Act of 1940) for the registrant and have:

(a)   Designed such disclosure controls and procedures, or caused such disclosure controls and procedures to be designed under our supervision, to ensure that material information relating to the registrant, including its consolidated subsidiaries, is made known to us by others within those entities, particularly during the period in which this report is being prepared;

(b)   [Omit] until after the first Form N-CSR filed after November 15, 2004;

(c)   Evaluated the effectiveness of the registrant's disclosure controls and procedures and presented in this report our conclusions about the effectiveness of the disclosure controls and procedures, as of a date within 90 days prior to the filing date of this report, based on such evaluation; and

(d)   [Omit] until after the first Form N-CSR filed after November 15, 2004; and

5.   The registrant's other certifying officer(s) and I have disclosed to the registrant's auditors and the audit committee of the registrant's board of directors (or persons performing the equivalent functions):

(a)   All significant deficiencies and material weaknesses in the design or operation of internal control over financial reporting which are reasonably likely to adversely affect the registrant's ability to record, process, summarize, and report financial information; and

(b)   Any fraud, whether or not material, that involves management or other employees who have a significant role in the registrant's internal control over financial reporting.

Date: October 22, 2004	/s/ David J. Schulte
	David J. Schulte President

CERTIFICATION

I, Terry C. Matlack, certify that:

1.   I have reviewed this report on Form N-Q of Tortoise Energy Infrastructure;

2.   Based on my knowledge, this report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by this report;

3.   Based on my knowledge, the schedules of investments included in this report fairly present in all material respects the investments of the registrant as of the end of the fiscal quarter for which the report is filed;

4.   The registrant's other certifying officer(s) and I are responsible for establishing and maintaining disclosure controls and procedures (as defined in Rule 30a-3(c) under the Investment Company Act of 1940) for the registrant and have:

(a)   Designed such disclosure controls and procedures, or caused such disclosure controls and procedures to be designed under our supervision, to ensure that material information relating to the registrant, including its consolidated subsidiaries, is made known to us by others within those entities, particularly during the period in which this report is being prepared;

(b)   [Omit] until after the first Form N-CSR filed after November 15, 2004;

(c)   Evaluated the effectiveness of the registrant's disclosure controls and procedures and presented in this report our conclusions about the effectiveness of the disclosure controls and procedures, as of a date within 90 days prior to the filing date of this report, based on such evaluation; and

(d)   [Omit] until after the first Form N-CSR filed after November 15, 2004; and

5.   The registrant's other certifying officer(s) and I have disclosed to the registrant's auditors and the audit committee of the registrant's board of directors (or persons performing the equivalent functions):

(a)   All significant deficiencies and material weaknesses in the design or operation of internal control over financial reporting which are reasonably likely to adversely affect the registrant's ability to record, process, summarize, and report financial information; and

(b)   Any fraud, whether or not material, that involves management or other employees who have a significant role in the registrant's internal control over financial reporting.

Date: October 22, 2004	/s/ Terry C. Matlack
	Terry C. Matlack Treasurer

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) Tortoise Energy Infrastructure Corporation

By (Signature and Title)  /s/ David J. Schulte
                                                   David J. Schulte, President

Date October 22, 2004

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/ David J. Schulte

David J. Schulte, President

Date  October 22, 2004

By (Signature and Title)* /s/ Terry C. Matlack
                                                    Terry C. Matlack, Treasurer

Date October 22, 2004

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