A numerical simulation and analysis was performed to investigate the effect of absorber and buffer layer band gap grading and on a Copper-Indium-Gallium-Diselenide (CIGS) solar cell. The software used is the Solar Cell Capacitance Simulator (SCAPS). The absorber and buffer layer energy band structures' effect on the cell's output parameters such as open circuit voltage, short circuit current density, fill factor and efficiency were extensively simulated. Two structures of the energy band gap were simulated and studied for each of the absorber and buffer layer. The simulation was done on the uniform structure in which the energy band gap is constant throughout the layer. It was then continued on the cell with graded band structure, where the energy band gap of the material is varied throughout the layer. It was found that the cell with graded band structure in absorber and buffer layer had demonstrated higher efficiency and better performance in comparison with the cell with uniform band gap structure.