Abstract: Let R be a ring, m and n be no-negative integers with m≤n. We prove that the triple (GFC_m,P_n,P^⊥_m∩GFC_n) is a hereditary Hovey triple in category GFC_n, the corresponding homotopy category is (GFC_m∩P^⊥_m)/(P_m∩P^⊥_m)=GFC/P, where P_n is the class of modules of projective dimension ≤n and GFC_n is the class of modules of Gorenstein FC projective dimension ≤n.

Key words: Gorenstein FC-projective module, exact model structure, cotorsion pair