Fuel cell is an emerging area in the field of renewable alternate energy sources. The operation of a fuel cell involves fluid flow, heat transfer, mass transfer processes and the electrochemical reaction. All the above processes are coupled and they take place in a small region of space making the system complex. The performance of a fuel cell can be studied by experiments and numerical modeling. In the present project, an attempt is made to mathematically model the performance of a Polymer Electrolyte Membrane (PEM) fuel cell using lumped and control volume approach. The various processes that take place inside the gas diffusion layer of anode and cathode, catalyst and membrane of the fuel cell are represented using governing equations based on the mass and energy conservation principles and electrochemical reactions. The equation that is used to represent the diffusion phenomena in the GDL is solved using the Finite Difference Method. The present model is capable of predicting the performance of the PEM fuel cell in close agreement with numerical model based on CFD approach with a maximum of 30% error.