The kernel polynomial method is employed to study the disorder effects of impurities on the superconductivity of double-layer graphene. The Bogoliubov-de-Gennes equations are solved self-consistently by the kernel polynomial method, and the spatial fluctuations of the superconducting order parameters caused by disorder are obtained. Furthermore, we calculate the density of states, the optical conductivity and the general inverse participation ratio, and we find that the energy gap in the density of states can be constrained by increasing disorder, accompanied with the disappearance of the Drude weight in optical conductivity. We also find that the electron states are Anderson localized by disorder and the superconductor-insulator transition happens in double-layer graphene.