Stress induced by an excessive difference in pressure between the air and the hydrogen in polymer electrolyte fuel cells degrades membrane durability. Controlling such stress improves the durability and solves one of the problems hampering commercialization of fuel cell electric vehicles. Hydrogen pressure can be raised more rapidly than the air pressure by regulating the pressure of the high-pressure hydrogen storage tank. However, the response for reducing the hydrogen pressure varies depending on the level of current generation. The air pressure can be reduced rapidly by releasing air, whereas it takes longer to raise the air pressure owing to compression of the air taken in from the atmosphere. The method proposed here for designing the control system of the air pressure and mass flow rate assumes that the system 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. 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 application of a sliding mode control theory for controlling the air pressure and flow control system using the mathematical model. It then explains the configuration of the control system for sensing the differential pressure within a specified range. Experimental results are finally presented to validate the control performance achieved with the proposed design method.