This paper describes a method of configuring a control system for keeping the differential pressure of the hydrogen and air supplied to a fuel cell within a specified range. The proposed method assumes that the control system of the air pressure and mass flow rate is based on the use of a mathematical model, whereas the hydrogen pressure control system does not employ a mathematical model and treats the consumption of hydrogen during power generation as a disturbance. When hydrogen consumption due to power generation is treated as a disturbance, the responsiveness of the hydrogen pressure and air pressure varies depending on the amount of power being generated. Therefore, the air pressure is predicted using transfer functions and the hydrogen pressure is made to follow the predicted value. In addition, the air pressure is made to follow the larger of either the reference pressure or the hydrogen pressure. This paper first describes the derivation of the mathematical model of the air supply system. The mathematical model is then used to design a sliding mode control system based on the two variables of the air pressure and mass flow rate. The method of configuring the differential air and hydrogen pressure control system is then explained, and experimental results are presented to validate the proposed design method.