In this paper, as a generalization of the notion of maximal Cohen-Macaulay module over a local ring $R$, we introduce a concept of relative maximal Cohen-Macaulay module with respect to an ideal of $R$. Then, we investigate some properties and characterizations of such modules and as an application of them, we provide generalization and improvement for the results cite[Theorem 3.1]{KAW} and cite[Theorem 1.11]{KHY}.