  Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative
ring with identity and $M$ a graded $R$-module. In this paper, we introduce the
concept of graded $I_{e}$-prime submodule as a generalization of a graded prime
submodule for $I=\oplus_{g\in G}I_{g}$ a fixed graded ideal of $R$. We give a
number of results concerning of these classes of graded submodules and their
homogeneous components. A proper graded submodule $N$ of $M$ is said to be a
graded $I_{e}$-prime submodule of $M$ if whenever $% r_{g}\in h(R)$ and
$m_{h}\in h(M)$ with $r_{g}m_{h}\in N-I_{e}N,$ then either $r_{g}\in (N:_{R}M)$
or $m_{h}\in N.$
