ANNALY CAPITAL MANAGEMENT, INC. AND SUBSIDIARIES

Exhibit 32.1

ANNALY CAPITAL MANAGEMENT, INC.

1211 AVENUE OF THE AMERICAS

NEW YORK, NEW YORK 10036

CERTIFICATION

PURSUANT TO SECTION 906 OF THE

SARBANES-OXLEY ACT OF 2002, 18 U.S.C. SECTION 1350

In connection with the quarterly report on Form 10-Q of Annaly Capital Management, Inc. (the “Company”) for the period ended March 31, 2015 to be filed with Securities and Exchange Commission on or about the date hereof (the “Report”), I, Wellington J. Denahan, Chief Executive Officer of the Company, certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, 18 U.S.C. Section 1350, that:

1. The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

2. The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company at the dates of, and for the periods covered by, the Report.

It is not intended that this statement be deemed to be filed for purposes of the Securities Exchange Act of 1934.

/s/ Wellington J. Denahan

Wellington J. Denahan

Chairman and Chief Executive Officer

May 7, 2015