A one-dimensional, dynamic proton exchange membrane fuel cells stack model is developed in this paper, where the transports of reactant and water (in both liquid and vapor phase) are described by partial differential equations (PDEs) in gas diffusion layers (GDLs) of both anode and cathode, and the lumped model is applied to channels and MEA. The boundary conditions needed for PDEs in GDLs are provided by the lumped model. In addition, the convection term is considered in PDEs for GDLs to describe the convection effect on hydrogen gas purge process on the anode side. As a result, the purge effect under medium current density (corresponding to ohmic polarization dominated region) can be simulated in an efficient manner by improving the mass transfer and reducing the effect of water back diffusion from cathode to anode. The presented gas purge model is validated by the experimental data obtained from our laboratory as well as other research group. The influence factors to the gas purge schedule on the anode side, such as the purge interval and purge time, are investigated as well.