Abstract: Let R be a ring, and S be a multiplicative subset of R. Firstly, we introduce the notion of Gorenstein u-S-injective modules by mean
s of the theory of Hom functors. Secondly, we study the homological properties of Gorenstein u-S-injective modules by using the u-S-Five Lemma and the method of constructing pull-back diagrams. Particalarly, it is shown that an R-module M is Gorenstein u-S-injective if and only if Extⁱ_R(E,M) is u-S-torsion module for any u-S-injective R-module E and any integer i>0, and M admits a proper left u-S-injective-resolution. The class of Gorenstein u-S-injective modules is closed under finite direct sums.

Key words: u-S-injective module, Gorenstein u-S-injective module, u-S-torsion module