Let R be an associative ring with identity. A right R–module M is called generalized principally quasi–Baer if for any m ∈ M, rR(m R) is left s– unital as an ideal of R and the ring R is said to be right (left) generalized principally quasi–Baer if R is a generalized principally quasi–Baer right (left) R–module. In this paper, we investigate properties of generalized principally quasi–Baer modules and right (left) generalized principally quasi–Baer rings.