Abstract: The notion of X-strongly Gorenstein projective module was defined. It was proved that a module is X-Gorenstein projective if and only if it is a direct summand of some X-strongly Gorenstein projective module. Furthermore, some basic properties of X-strongly Gorenstein modules were obtained. And some results about strongly Gorenstein modules were generalized or strengthened.

Key words: Gorenstein projective modules, strong Gorenstein projective modules, X-Gorenstein projective modules, X-strongly Gorenstein projective module