This paper presents a nonlinear control strategy for the well-known nonlinear fifth-order model of a proton exchange membrane (PEM, also known as polymer electrolyte membrane) fuel cell (PEMFC). We propose a simple sliding mode technique for this nonlinear model to keep pressures of hydrogen and oxygen at the desired values despite of changes of the fuel cell current. It is known that large deviations between hydrogen and oxygen partial pressures can damage the fuel cell membrane. The controller keeps the pressure difference between hydrogen and oxygen as small as possible after reaching steady state. Since the fuel cell current is considered as a disturbance, we apply a sliding mode control technique that copes well with external disturbances and uncertainties. Moreover, the proposed controller outperforms the controller previously proposed for this fuel cell model.