Let G be a group, R be a G-graded commutative ring with identity, M be a unitary graded R-module, Spec_g(R) be the set of graded prime ideals of R, and Cl.Spec_g(M) be the set of all graded classical prime submodules of M. In this paper among other things, the author studied the Zariski topology on both and Cl.Spec_g(M), and investigate some properties of the Zariski topology on Cl.Spec_g(M) and some conditions under which the graded classical prime spectrum of M is a spectral for its Zariski topology.