The effects of anode, cathode, and cooling channels for a Proton Exchange Membrane Fuel Cell (PEMFC) on flow fields have been investigated numerically. Continuous open-faced fluid flow channels formed in the surface of the bipolar plates traverse the central area of the plate surface in a plurality of passes such as a serpentine manner. The pressure distributions and velocity profiles of the hydrogen, air and water channels on bipolar plates of the PEMFC are analyzed using a two-dimensional simulation. The conservation equations of mass, momentum, and energy in the three-dimensional flow solver are modified to include electro-chemical characteristics of the fuel cell. In our three-dimensional numerical simulations, the operation of electro-chemical in Membrane Electrolyte Assembly (MEA) is assumed to be steady-state, involving multi-species. Supplied gases are consumed by chemical reaction. The distributions of oxygen and hydrogen concentration with constant humidity are calculated. The concentration of hydrogen is the highest at the center region of the active area, while the concentration of oxygen is the highest at the inlet region. The flow and thermal profiles are evaluated to determine the flow patterns of gas supplied and cooling plates for an optimal fuel cell stack design.