Abstract: The notions of W^⊥_R-Gorenstein injective module and W^⊥_R-Gorenstein injective dimension respect to a generalized tilting moduleW_R,and it is prove that the W^⊥-Gorenstein injectivity is preserved under Frobenius extensions, that is, for a Frobenius extension S/R and an R-ModuleM_R,M_R is W^⊥_R-Gorenstein injective if and only ifMⓧ_RS_S is (Wⓧ_RS_S)^⊥_S-Gorenstein injective. Some properties of W^⊥_R-Gorenstein injective dimension are obtained. Furtheremore,as an applications, some valuable corollaries about some classical homological dimension as applications.

Key words: feneralized tilting modules, Frobenius extension, W^⊥-Gorenstein injective modules