Summary: Let \(G\) be a monoid with identity \(e\), and let \(R\) be a \(G\)-graded commutative ring. Graded weakly prime ideals in a \(G\)-graded commutative ring have been introduced and studied in [\textit{S. E. Atani}, On graded weakly primary ideals, quasi-groups and related systems (to appear)]. Here we study graded weakly prime submodules of a \(G\)-graded \(R\)-module. A number of results concerning of these class of submodules are given. For example, we give some characterizations of homogeneous components of graded submodules.