Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the Registration Statements (No. 333-234235, No. 333-252078 and No. 333-252903) on Form S-3 and Registration Statements (No. 333-203703, No. 333-210369, No. 333-216858, No. 333-224062, No. 333-230041, No. 333-236794 and No. 333-252743) on Form S-8 of KemPharm, Inc. of our report dated March 11, 2021 relating to the financial statements of KemPharm, Inc., appearing in this Annual Report on Form 10-K of KemPharm, Inc. for the year ended December 31, 2020.

/s/ RSM US LLP

Orlando, Florida

March 11, 2021