In this paper, a Backstepping controller is proposed for the air supply system of polymer electrolyte membrane fuel cell (PEMFC). The control objective is to regulate the oxygen excess ratio to its optimal value despite the disturbances introduced by rapid transitions in the cell output current. This improves the PEMFC efficiency, reduces its losses, and prevents oxygen deficiency. To describe the airflow dynamic behaviors, a fourth-order PEMFC model is established, and then a Backstepping controller is proposed to track the optimal excess oxygen ratio. The closed-loop performances are established using Lyapunov stability tools. The efficiency of the suggested control strategy is validated, under Matlab-Simulink environment, by conducting a comparison with conventional controllers such as PID, and Super-Twisting Controller (STC). These simulations illustrate the supremacy of the proposed controller when the PMFC is subjected to various operating conditions.