In this paper we introduce a new generalization of small submodules,namelyγ-small submodules. We call a submoduleKof a moduleM,γ-small providedM=K+LwithM/Lnoncosingular, impliesM=L. Applying this concept, we define a generalization of lifting modulesentitledγ-lifting modules and investigate their some general properties.It is proved that any supplement submodule of aγ-lifting module isγ-lifting
