The polar Kerr rotation, Kerr ellipticity and optical constant n and k change regularly with the increase of Mn doping in Pt layer of Pt/Co multilayers. Through calculation and analyses, in heavy Mn doping the change of the Kerr rotation is due to the off-diagonal elements of dielectric tensor. However, in light Mn dop ing the change of Kerr rotation results from the change in the magneto-optical a nd optical constants. The enhanced magneto-optical Kerr rotation is due to the e nhancement of Pt spin-orbit coupling. The variation of Pt spin-polarization resu lts in the change of diagonal and off-diagonal elements of dielectric tensor.