In this paper, an effective combined finite element-upwind finite volume method is studied for a three-dimensional transient multiphysics transport model of a proton exchange membrane fuel cell (PEMFC), in which Navier–Stokes–Darcy coupling flow, species transports, heat transfer, electrochemical processes, and charge transports are fully considered. Multiphase mixture (M2) formulation is employed to define the involved two-phase model. Kirchhoff transformation is introduced to overcome the discontinuous and degenerate water diffusivity that is induced by the M2 model. By means of an adaptive time-stepping fourth-order multistep backward differencing formula (BDF), we design an effective temporal integration scheme to deal with the stiff phenomena arising from different time scales. In addition, all the governing equations are discretized by a combined finite element-upwind finite volume method to conquer the dominant convection effect in gas channels, while the diffusion and reaction effects are still dealt with by finite element method. Numerical simulations demonstrate that the presented techniques are effective to obtain a fast and convergent nonlinear iteration within a maximum 36 steps at each time step; in contrast to the oscillatory and nonconvergent iteration conducted by commercial CFD solvers and standard finite element/finite volume methods.