Abstract: Let R be a ring, and S be a multiplicative subset of R. Firstly, based on the u-S-flat modules, we introduce the concept of Gorenstein u-S-flat modules,  and  use the long exact sequence theorem and the properties of u-S-flat modules to study the homological properties of Gorenstein u-S-flat modules, and give equivalent characterizations of Gorenstein u-S-flat modules. Secondly, we  prove that the class of Gorenstein u-S-flat modules is projective solvable class if and only if it is closed with respect to extensions.

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