A three dimensional numerical model to predict the flow and transport of mixtures and also the electrochemical reactions in polymer electrolyte membrane (PEM) fuel cells is developed. The numerical computation is base on vorticity- velocity method. Governing equations for the flow and transport of mixtures are coupled with the equations for electrochemical reactions and are solved simultaneously including production and condensation of vapor. Fuel cell performance predicted by this calculation is compared with the experimental results and resonable agreements are achieved.