Overseas Shipholding Group (OSG): BHR Capital Reduces Stake

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 13D

Under the Securities Exchange Act of 1934

(Amendment No. 2)*

Overseas
Shipholding Group, Inc.

(Name of Issuer)

Class A Common Stock (par value $0.01 per share)

(Title of Class of Securities)

69036R103

(CUSIP Number)

Michael Falk

BHR Capital LLC

733
Third Avenue, 15th Floor

New York, NY 10017

(212) 378-0830

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

December 15, 2015

(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 §§ 240.13d-1(e), 240.13d-1(f) or 240.13d-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 Section
240.13d-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, as amended (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 5 of the Schedule 13D is amended and restated in its entirety
as follows:

(a) Rows 11-13 of the cover page of this Schedule 13D with respect to each Reporting Person is incorporated herein by reference.

The Reporting Persons beneficial ownership include 3,078,181 shares of Class A Common Stock issuable upon exercise of 16,200,956 Class A Warrants. The
percentage of Class A Common Stock beneficially owned is based on approximately 65,612,275 shares of Class A Common Stock outstanding. The Reporting Persons derived this outstanding share amount based on 393,673,653 shares of Class A Common Stock
outstanding as of May 5, 2016, as reported in the Issuers Form 10-Q filed on May 10, 2016, and giving effect to a 1:6 reverse stock split that occurred on June 13, 2016, as reported in the Issuers Form 8-K filed on June 7, 2016.

(b) Rows 7-10 of the cover page of this Schedule 13D with respect to each Reporting Person is incorporated herein by reference.

(c) Schedule A sets forth the Reporting Persons transactions in the Class A Common Stock and Class A Warrants in the sixty days prior to December 15,
2015, March 29, 2016, May 2, 2016 and June 13, 2016. On June 13, 2016, the Issuer effected a 1:6 reverse stock split. As a result of the reverse stock split, (i) BHR Master and BHR-OSG directly hold 398,957 and 972,126 shares of Class A Common
Stock, respectively and (ii) the 16,200,956 Class A Warrants held by BHR-OSG became exercisable for 3,078,181 shares of Class A Common Stock.

(d) Not applicable.

(e) Not applicable.

SIGNATURES

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

Dated: July 13, 2016

Schedule A