In this paper we introduce the concept of tCC-modules which is a proper generalization of (t-)lifting modules. Let M be a module over a ring R. We call M a tCC-module (related to tcoclosed submodules) provided that for every t-coclosed submodule N of M, there exists a direct summand K of M such that M = N + K and N ∩ K\ll K. We prove that a module with (D_3) property is tCC if and only if every direct summand of M is tCC. It is also shown that an amply supplemented module M is tCC if and only if M decomposed to Z2(M) and a submodule L of M that both of them are tCC.
