For a given right R-module M, a right R-module N is called a pseudo-M-c-injective module if every monomorphism from a closed submodule of M to N can be extended to a homomorphism from M to N. We develop, in this paper, pseudo-c-injectivity as a generalization of c-injectivity. We give several properties of pseudo-M-c-injective module and quasi-pseudo-c-injective module. Beside surveying several properties of pseudo-M-c-injective modules, we find out some relations of quasi-pseudo-c-injectivity with some notation such as CS-modules, uniform modules.