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 October 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 ¨

Senior Unsecured Notes Indenture

On October 16, 2025, Danaos Corporation (the “Company”) closed its previously announced offering of $500 million aggregate principal amount of its 6.875% senior notes due 2032 (the “Notes”). The Notes bear interest at a rate of 6.875% per year, payable in cash on March 1 and September 1 of each year, commencing March 1, 2026, and will mature on October 15, 2032. The Notes were issued pursuant to an Indenture, dated as of October 16, 2025, between the Company and Citibank, N.A., London Branch, as trustee, paying agent, registrar and transfer agent (the “Indenture”), which is filed herewith as Exhibit 99.1.

The Company intends to use the net proceeds from the offering to (i) redeem in full the $262.8 million outstanding principal amount of the Company’s 8.500% Senior Notes due 2028 (the “2028 Notes”) on or about March 1, 2026, (ii) repay in full the outstanding principal amount under its BNP Paribas/Credit Agricole $130 million Secured Credit Facility on December 1, 2025, (iii) repay in full the outstanding principal amount under its Alpha Bank $55.25 million Secured Credit Facility on December 1, 2025, (iv) to pay costs, fees and expenses related to the refinancing, including commissions, placement, financial advisory fees and other transaction costs and professional fees, and (v) for general corporate purposes.

This report on Form 6-K does not constitute a notice of redemption with respect to the 2028 Notes and investors are urged to refer to the relevant notice of redemption, when available, for more information regarding the conditions precedent to such redemption, redemption price, record date and redemption date.

EXHIBIT INDEX

99.1 Indenture, dated as of October 16, 2025, between Danaos Corporation and Citibank, N.A., London Branch, as trustee, paying agent, registrar and transfer agent

99.2 Form of Danaos Corporation 6.875% Senior Notes due 2032 (included in Exhibit 99.1)

EXHIBIT INDEX

*****

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: October 16, 2025

	DANAOS CORPORATION

	By:	/s/ Evangelos Chatzis
	Name:	Evangelos Chatzis
	Title:	Chief Financial Officer

Danaos Corp 6-K