  In the paper, we mainly connect the Gorenstein derived equivalence and stable
functors of Gorenstein projective modules. Specially, we prove that a
Gorenstein derived equivalence between CM-finite algebras A and B can induce a
stable functor between the factor categories A-mod/A-Gproj and B-mod\B-Gproj.
Furthermore, the above stable functor is an equivalence when A and B are
Gorenstein.
