In this work, a front graded band gap of CIGS absorber is simulated where a spatial variation of the band gap energy decreases from a maximum value Egmax at the limit of the junction to a minimum value Egmin at the vicinity of the back contact within the length of the CIGS layer. An effective absorption coefficient due to this variation was defined. It will be seen that this graded profile contributes to improve the open circuit voltage Voc owing to the effect of the created quasi-electrical field on the photo generated carriers which lead to an improvement of the efficiency. However, a reduction of the short current density Jsc is noted. We also demonstrate that the absorber thickness has an impact on the parameters above mentioned. This simulation allowed us to optimize the grading profile which consists on Egmin, Egmax and the absorber thickness d in order to reach a desired significant improvement of Voc and efficiency.