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 2025

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 ¨

INFORMATION CONTAINED IN THIS FORM 6-K REPORT

On May 30, 2025, Charalampos Pampoukis was appointed as a Class III director of Danos Corporation (the “Company”), increasing to seven the number of directors currently serving on the Company’s Board of Directors.

Charalampos Pampoukis is a prolific scholar and legal writer who holds numerous accolades in the field of international trade law. He is currently the Director at the Hellenic Institute of International and Foreign Law at the National and Kapodistrian University of Athens, where he teaches courses in Private International Law and International Trade Law. He has previously taught at the Hague Academy of International Law, and has authored three major treatises on private international and business law and arbitration,. Charalampos Pampoukis has been a licensed attorney since 1984 and is a founder and managing partner of a law firm, PMN-Pampoukis — Maravelis — Nikolaidis & Associates (Alpha Law), recognized for its international litigation and international corporate practice. Previously, Charalampos Pampoukis served as Secretary General in the Ministry of Foreign Affairs (1999 – 2000), Minister of State and to Prime Minister (2009 – 2011) and Minister Alternate in Maritime Affairs (2011) in Greece and was honored by the President of the French Republic by being nominated as Commandeur de la Légion d’honneur. Charalampos Pampoukis currently serves on the board of directors of Aktor Group of Companies, Athens International Airport and Alter Ego Media, all of which are listed on the Athens Stock Exchange, and took an active role in the successful listing of the latter two on the Athens Stock Exchange. Charalampos Pampoukis studied law in Paris (Paris I — Panthéon — Sorbonne) from where he also obtained a PhD with honors in 1990 (Docteur d’Etat en droit).

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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. 333-270457) filed with the SEC on March 10, 2023.

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 2, 2025