Aiming at the problem that the dynamic performance of the fuel cell air supply system is susceptible to load changes and external environmental factors, a tandem-type control strategy combining super-helical sliding mode control and terminal sliding mode control is designed. A control-oriented fifth-order dynamic model is established, and the control problem of tracking the optimal oxygen excess ratio, maximum net output power and cathode pressure measurement of the air supply system during load change is proposed; the optimal expectation value is extracted and the controller is designed, and the closed-loop stability is verified using the Lyapunov method. Simulation analysis shows that the constructed observer perturbation estimate is within 0.01% error from the theoretical actual value. Compared with PID control, the response time of tracking the optimal expected value of the oxygen excess ratio is improved by 6.9%, the maximum net power output is increased by 0.2%, and the response time of cathode pressure is improved by 60%. From the results, it can be concluded that the strategy of this paper can effectively control the oxygen excess ratio of the gas supply system to track the optimal desired value and output the maximum net power when the load changes, can accurately and rapidly estimate the cathode pressure, can better estimate the perturbation, and has a strong anti-disturbance ability.