The Proton Exchange Membrane Fuel Cell (PEMFC) is the most widely used engine in fuel cell vehicles. For PEMFC, whether the supply of oxygen for cathode is adequate or not is a critical factor for its net output power and service life, and the proper control of air supply mass flow and pressure can effectively improve its system performance and efficiency. At present, fuel cells need to reduce the mass and volume and increase the power density. Therefore, it is necessary to increase the air supply pressure for PEMFC. But at the same time, many auxiliary devices are appended to the system to provide high-pressure air, such as air compressor, intercooler, and back pressure valve, which make the control of the entire air supply system very complicated. So an excellent control algorithm is needed. This paper mainly focuses on the air supply system of a 85kW high-pressure PEMFC stack, researches its control algorithms, and discusses and studies the control effects of the feedforward control and the feedback control. For the feedback control, the traditional PID method is firstly studies, and the relationship between the fuel cell stack’s pressure and mass flow under different working conditions is analyzed. After that, the decoupled PID control algorithm is used to eliminate the mutual coupling among different channels. Then, the paper researches the model predictive control (MPC) algorithm and compares its effects with those of the PID algorithm. Finally, the linear variable parameter (LPV) model is constructed as the predictive model of MPC. This paper also studies the control effects of adaptive MPC algorithm and single-point MPC algorithm, which shows that the former can gain control effects with higher precision of the stack’s pressure and mass flow in the whole working condition range.