The optical properties of graphene have been studied using first-principle density functional theory (DFT) calculations. The dielectric function, refractive index and birefringence in parallel and perpendicular polarization of electric field to the plane of graphene under 0 GPa, 5 GPa and 10 GPa pressures have been studied. The values of these parameters at 5 GPa and 10 GPa have been calculated for the first time. In parallel direction, the threshold energy is blue shifted towards the IR region, whereas in perpendicular direction, it is red shifted towards the UV region. The calculated values are in good agreement with the earlier reported values.