Let G be a group. Let R be a G-graded commutative ring with identity and M be a G-graded multiplication module over R. A proper graded submodule Q of M is semiprime if whenever $I^nK{subseteq}Q$, where $I{subseteq}h(R)$, n is a positive integer, and $K{subseteq}h(M)$, then $IK{subseteq}Q$. We characterize semiprime submodules of M. For example, we show that a proper graded submodule Q of M is semiprime if and only if grad$(Q){cap}h(M)=Q+{cap}h(M)$. Furthermore if M is finitely generated then we prove that every proper graded submodule of M is contained in a graded semiprime submodule of M. A proper graded submodule Q of M is said to be almost semiprime if (grad(Q)$cap$h(M))n(grad$(0_M){cap}h(M)$) = (Q$cap$h(M))n(grad$(0_M){cap}Q{cap}h(M)$). Let K, Q be graded submodules of M. If K and Q are almost semiprime in M such that Q + K $ eq$ M and $Q{cap}K{subseteq}M_g$ for all $g{in}G$, then we prove that Q + K is almost semiprime in M.