Using the renewable energy resources has attracted the attention of researchers and automobile companies, because of limited fossil fuel resources, low efficiency of internal combustion engines and their environmental pollutions. By using the fuel cell systems instead of internal combustion engines can be partially overcome these problems. In this regard, the present article examines a PEM fuel cell system for using in an urban vehicle. In the first part of this article, by using the real component of system, the fuel cell system components including stack, membrane humidity of air and hydrogen, air compressor, water pump and pump cooler stack has been modeled in MATLAB Simulink environment. The mentioned model can evaluate the power consumption of system and its peripheral component and also required water, hydrogen and air for system. At the base case and the current density of 0.7A / cm2, 14% of power productions of stack are consumed by auxiliaries units. At this current density, the overall and net system efficiencies are 48.15% and 34.3%. In the second part of this article, the system from the point of view of the first law of thermodynamics has been optimized with objective functions of maximum output power and maximum efficiency. The results indicate that first model search method is best method for optimization, second at the Optimization with the aim of maximum power, pure power and system efficiency are increased 11.9% and 4% respectively and the power consumption by auxiliary unit is reduced 42%.