Exhibit 32.1

CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the annual report of Atlas Air Worldwide Holdings, Inc. (the “Company”), on Form 10-K for the period ended December 31, 2018, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, William J. Flynn, President and Chief Executive Officer of the Company, certify, to the best of my knowledge, pursuant to Rule 13a-14(b) under the Securities and Exchange Act of 1934 and 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

1. the Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities and 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.

/s/ William J. Flynn

William J. Flynn

President and Chief Executive Officer

Dated: February 19, 2019