A three dimensional, electrochemical mathematical model is herein developed to simulate the non-isothermal temperature distribution and two-phase flow for liquid water transport processes in a proton exchange membrane fuel cell (PEMFC). The proposed model includes water phase changes and transport mechanisms in the porous region of the catalyst layer (CL), gas diffusion layer (GDL), and flow channel, and heat transfer within the membrane electrode assembly (MEA) and collector plate. The effects of the relative humidity of inlet gases, operating pressure, and temperature on fuel cell performance are numerically simulated. The results show that relatively high operating pressure increases the oxygen diffusion rate to some degree, which has beneficial effects on fuel cell performance. Meanwhile, relatively high operating temperature increases electrode kinetics and reduces liquid water saturation, which also improves fuel cell performance. Thermal management and water management are essential owing the significant effects that the temperature distribution and liquid water saturation state have on cell performance. (C) 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.