Let G be a group with identity e, R be a commutative G-graded ring with unity 1 and M be a G-graded unital R-module. In this article, we introduce the concept of graded 1-absorbing prime submodule. A proper graded R-submodule N of M is said to be a graded 1-absorbing prime R-submodule of M if for all non-unit homogeneous elements x, y of R and homogeneous element m of M with xym ∈ N, either xy ∈ (N :R M) or m ∈ N. We show that the new concept is a generalization of graded prime submodules. At the same time it is a special graded 2-absorbing submodule. Several properties of a graded 1-absorbing prime submodule have been obtained. We investigate graded 1-absorbing prime submodules when the components {Mg : g ∈ G} are multiplication Re-modules.