Let M be a left module over a ring R andI an ideal of R. M is called an I-supplemented module (finitely I-supplementedmodule) if for every submodule (finitely generated submodule ) X of M, there isa submodule Y of M such that $X + Y = M$, $X \cap Y \subseteq IY$ and $X \capY$ is PSD in Y. This definition generalizes supplemented modules and $\delta$-supplementedmodules. We characterize I-semiregular, I-semiperfect and I-perfect rings whichare defined by Yousif and Zhou [12] using I-supplemented modules. Some wellknown results are obtained as corollaries.