Report of Foreign Issuer Pursuant to Rule 13a-16 or 15d-16 (6-k)

UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 6-K

REPORT OF FOREIGN PRIVATE ISSUER PURSUANT TO RULE 13a-16 OR

15d-16 UNDER THE SECURITIES EXCHANGE ACT OF 1934

For the month of June 2022

Commission File Number 001-33060

DANAOS CORPORATION

(Translation of registrant’s name into English)

Danaos Corporation

c/o Danaos Shipping Co. Ltd.

14 Akti Kondyli

185 45 Piraeus

Greece

Attention: Secretary

011 030 210 419 6480

(Address of principal executive office)

Indicate by check mark whether the registrant files or will file annual reports under cover of Form 20-F or Form 40-F.

Form 20-F x Form 40-F ¨

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(1): ¨

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(7): ¨

Share Repurchase Program

The Board of Directors of Danaos Corporation (the “Company”) has approved a share repurchase program and authorized the officers of the Company to repurchase, from time to time, up to $100 million of the Company’s common stock. Shares may be purchased in open market or privately negotiated transactions, at times and prices that are considered to be appropriate by the Company, and the program may be suspended or discontinued at any time.

*****

This report on Form 6-K is hereby incorporated by reference into the Company’s (i) Registration Statement on Form F-3 (Reg. No. 333-237284) filed with the SEC on March 19, 2020, (ii) the post-effective Amendment to Form F-1 in the Registration Statement on Form F-3 (Reg. No. 333-226096) filed with the SEC on March 6, 2019, (iii) Registration Statement on Form F-3 (Reg. No. 333-174494) filed with the SEC on May 25, 2011, (iv) Registration Statement on Form F-3 (Reg. No. 333-147099), the related prospectus supplements filed with the SEC on December 17, 2007, January 16, 2009 and March 27, 2009, (v) Registration Statement on Form S-8 (Reg. No. 333-233128) filed with the SEC on August 8, 2019 and the reoffer prospectus, dated August 8, 2019, contained therein, (vi) Registration Statement on Form S-8 (Reg. No. 333-138449) filed with the SEC on November 6, 2006 and the reoffer prospectus, dated November 6, 2006, contained therein, (vii) Registration Statement on Form F-3 (Reg. No. 333-169101) filed with the SEC on October 8, 2010, (viii) Registration Statement on Form F-3 (Reg. No. 333-255984) filed with the SEC on May 10, 2021 and (ix) Registration Statement on Form F-3 (Reg. No. 333-263299) filed with the SEC on March 4, 2022.

SIGNATURES

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

Date: June 14, 2022