This paper proposes an actuator fault detection observer design method for a proton exchange membrane fuel cell (PEMFC) system described by delta operator form. In the first, a nonlinear mathematical model for the PEMFC system is proposed by using the mechanism analysis method, which includes the time delay, external disturbance and uncertainty to reduce the conservatism of the design. Then, in order to detect the actuator fault, the functional observer is constructed as the residual generator, and sufficient conditions for the stability of the error system are obtained by using the Lyapunov-krasovsky functional theory in terms of linear matrix inequalities (LMIs), so as to ensure the design of the required functional observer. Finally, simulation results are provided to show the effectiveness of the approach.