Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We hereby consent to the incorporation by reference in the Registration Statements on Form S-3 (No.333-181923) and Form S-8 (Nos. 333-177704, 333-170244, 333-158120, 333-143240, and 333-133405) of Atlas Air Worldwide Holdings, Inc. of our report dated February 13, 2013 relating to the financial statements, financial statement schedule and the effectiveness of internal control over financial reporting, which appears in this Form 10-K.

/s/ PricewaterhouseCoopers LLP

Florham Park, New Jersey

February 13, 2013