In this work, the notion of injectivity relative to a class of IQC sub modules (namely, IQC-injectivity) has been introduced and studied, which is a generalization quasi-injective module. This notion is closed under direct summands. Several properties and characterizations have been given.We provide a characterization of semi simple Artinian ring , SI-ring and Dedekind domain in terms of IQC-injective R-module
