This paper presents and studies the mathematical model of proton exchange membrane of fuel cell (PEMFC) using Matlab/SIMULINK software. The paper consists of the calculation of cell voltage, the double layer charging effect, dynamic response and thermodynamic response. This model is used to analyze the fuel cell behavior and the characteristic of output values at different parameters. Two characteristics involved in this paper which are transient and steady-state condition where the results are presented in graphical representation. The parameters for this model in this paper are based on Ballard-Mark-V fuel cell. The maximum power produced by the fuel cell is 3757 watt at load current of 261.4 Amps.