In order to improve the efficiency and service life of fuel cell, its multiple states must be precisely controlled. The fourth order nonlinear equation of controloriented fuel cell air system was established and the validity of model is verified. Then a non-singular terminal sliding mode control strategy based on global feedback linearization theory was proposed for the nonlinear and strong coupling characteristics of air supply system pressure and air flow. The feedback linearization transforms the nonlinear model into a linear model through the coordinated control of air compressor speed and back pressure valve opening, realizing the decoupling of cathode pressure and air flow. Considering the uncertain disturbance of air system in the complex environment, a proportional integral observer was designed to observe the disturbance to reduce the environmental impact. A non-singular sliding mode controller was further designed. The simulation results show that the error integrals of the cathode pressure and peroxide ratio of non-singular sliding mode control are less than those of the common sliding mode control and feedback linearization control, which significantly improves the accuracy and robustness of the fuel cell air supply control system and provides a reference for the future development of the high-precision fuel cell cathode air supply control system.