In the present study, fuel cell performance on the PEMFC cathode is investigated numerically. The modeling framework is assuming that the transport process is diffusion controlled and the convection transport is neglected. Both the single phase and two-phase flows are studied. The single phase, a 1-D, non-isothermal model is developed for various heat generation mechanisms, including irreversible heat due to electrochemical reactions, entropic heat, and Joule heating arising from the electrolyte ionic resistance. The thermal model is further coupled with the electrochemical and mass transport models. The computational domain includes the gas diffusion layer, the catalyst later and the membrane. The predicted results are validated with the experimental data of Liu et al. The effect of various operational parameters on the PEM fuel cell performance is investigated in detail. The results demonstrate the usefulness of this computational model as a design and optimization tool. For the two-phase simulations, the temperature is assumed to remain constant throughout the fuel cell. The reason is that the condensation and evaporation effect of the liquid water is not accounted for. Here, the phase change process is modeled as an equilibrium (i.e. infinitely fast) process, while the transport of liquid water is governed by pressure, surface tension and electro-osmotic drag. Results show that the inclusion of liquid water transport greatly enhances the predictive capability of the model.