UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 13D/A

Under the Securities Exchange Act of 1934

(Amendment No. 4)*

DUNE ENERGY, INC.

(Name of Issuer)

COMMON STOCK, PAR VALUE $0.001 PER SHARE

(Title of Class of Securities)

265338707

(CUSIP number)

David B. Charnin, Esq.

Strategic Value Partners, LLC

100 West Putnam Avenue

Greenwich, CT 06830

(203) 618-3500

(Name, Address and Telephone Number of Person Authorized to Receive Notices and Communications)

June 28, 2013

(Date of Event Which Requires Filing of this Statement)

If the filing person has previously filed a statement on Schedule 13G to report the acquisition that is the subject of this Schedule 13D, and is filing this schedule because of Rule 13d-1(e), 13d-1(f) or 13d-1(g), check the following box  ¨.

Note: Schedules filed in paper format shall include a signed original and five copies of the schedule, including all exhibits. See Rule 13d-7 for other parties to whom copies are to be sent.

The information required on the remainder of this cover page shall not be deemed to be “filed” for the purpose of Section 18 of the Securities Exchange Act of 1934 (the “Act”) or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

Item 1 of the Schedule 13D (as defined below) is hereby amended to add the following:

This Amendment No. 4 to the statement on Schedule 13D (this “Amendment No. 4”) amends and supplements the statement on Schedule 13D filed on December 22, 2011 (the “Original 13D”) with the United States Securities and Exchange Commission (the “SEC”), as amended on September 11, 2012 (the “Amendment No. 1”) and as subsequently amended on December 24, 2012 (the “Amendment No. 2”) and as subsequently amended on May 14, 2013 (the “Amendment No. 3” and collectively with the Original 13D, the Amendment No. 1 and the Amendment No. 2, the “Schedule 13D”), and relates to the common stock, par value $0.001 per share (“Common Stock”), of Dune Energy, Inc., a Delaware corporation (the “Issuer”). The address of the Issuer’s principal executive offices is: Two Shell Plaza, 777 Walker Street, Suite 2300, Houston, Texas 77002.

The information set forth in response to each separate Item below shall be deemed to be a response to all Items where such information is relevant.

Except as specifically provided herein, this Amendment No. 4 does not modify any of the information previously reported in the Schedule 13D. Capitalized terms used but not otherwise defined in this Amendment No. 4 shall have the meanings ascribed to them in the Schedule 13D.

Item 3 is hereby amended in its entirety as set forth below:

The Reporting Persons acquired the Common Stock reported herein pursuant to the Exchange Offer and the Stock Purchase Agreement. As of June 28, 2013, the Investment Vehicles had invested $50,116,276 (inclusive of brokerage commissions) in the Common Stock of the Issuer. The source of these funds internally generated funds of the Investment Vehicles.

Item 5 is hereby amended in its entirety as set forth below:

(a) – (b) According to the Issuer’s 10-Q filed with the SEC on November 5, 2013, there are approximately 71,476,811 shares of Common Stock outstanding as of November 5, 2013.

(i) As of the date hereof and as of June 28, 2013, Strategic Value Partners beneficially owns 17,917,244 shares of Common Stock, which constitutes approximately 25.1% of the Issuer’s outstanding shares of Common Stock. Strategic Value Partners does not have the sole power to vote or dispose of any shares of Common Stock. Strategic Value Partners has the shared power to vote and to dispose of 17,917,244 shares of Common Stock, which are held as follows: (i) SV Master Fund owns 14,422,225 shares of Common Stock held by High Ridge; (ii) SS Onshore Fund owns 887,244 shares of Common Stock directly; and (iii) SS Offshore Fund owns 2,607,775 shares of Common Stock held by Mardi Gras.

(ii) As of the date hereof and as of June 28, 2013, Special Situations beneficially owns 3,495,019 shares of Common Stock, which constitutes approximately 4.9% of the Issuer’s outstanding shares of Common Stock. Special Situations does not have the sole power to vote or dispose of any shares of Common Stock. Special Situations has the shared power to vote and to dispose of 3,495,019 shares of Common Stock, which are held as follows: (i) SS Onshore Fund owns 887,244 shares of Common Stock directly and (ii) SS Offshore Fund owns 2,607,775 shares of Common Stock held by Mardi Gras.

(iii) As of the date hereof and as of June 28, 2013, Mr. Khosla beneficially owns 17,917,244 shares of Common Stock held by the Strategic Value Partners and Special Situations, which constitutes approximately 25.1% of the Issuer’s outstanding shares of Common Stock. Mr. Khosla does not have the sole power to vote or dispose of any shares of Common Stock. Mr. Khosla has the shared power to vote and to dispose of 17,917,244 shares of Common Stock. Mr. Khosla disclaims beneficial ownership of such securities of the Issuer, except to the extent of his pecuniary interest in the Investment Vehicles, if any.

(c) Pursuant to the Stock Purchase Agreement, on June 28, 2013, High Ridge, Mardi Gras and SS Onshore Fund fulfilled an obligation to buy 1,325,356; 229,995; and 78,251 shares of Common Stock, respectively, from the Issuer in the form of the exercise of short put options (obligation to buy) for shares of Common Stock received upon the satisfaction of certain conditions of the Issuer in exchange for an aggregate consideration of $2,613,764.48. Other than the securities received by the Reporting Persons pursuant to the Stock Purchase Agreement, there have been no transactions with respect to the Shares during the sixty days prior to the date of this Schedule 13D by the Reporting Persons or, to their knowledge, by any executive officer or director of the Reporting Persons.

(d) No other person is known by any Reporting Person to have the right to receive or the power to direct the receipt of dividends from, or the proceeds from the sale of, the Common Stock beneficially owned by any Reporting Person.

(e) Not applicable.

SIGNATURE

After reasonable inquiry and to the best of my knowledge and belief, each of the undersigned hereby certifies that the information set forth in this statement is true, complete and correct.

December 16, 2013

ATTENTION:

Intentional misstatements or omissions of fact constitute Federal criminal violations (see 18 U.S.C. 1001).