  Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative
ring and $M$ a graded $R$-module. In this paper, we introduce the concept of
graded primary-like submodules as a new generalization of graded primary ideals
and give some basic results about graded primary-like submodules of graded
modules. Special attention has been paid, when graded submodules satisfies the
gr-primeful property, to find extra properties of these graded submodules.
