As a generalization of right p-injective rings, we introduce the notion of right Jcp-injective rings, i.e. for any right nonsingular element c of R and any right R-homomorphism g : cR → R, there exists m ∈ R such that g(ca) = mca for all a ∈ R. Some important results which are known for right p-injective rings are shown to hold for right Jcp-injective rings.