  The aim of this article is to introduce the concept of graded $2$-absorbing
coprimary submodules as a generalization of graded strongly $2$-absorbing
second submodules, and explore some properties of this class. A non-zero graded
$R$-submodule $N$ of a graded $R$-module $M$ is called a graded $2$-absorbing
coprimary $R$-submodule if whenever $x, y$ are homogeneous elements of $R$ and
$K$ is a graded $R$-submodule of $M$ such that $xyN\subseteq K$, then either
$x$ or $y$ is in the graded radical of $(K :_{R} N)$ or $xy\in Ann_{R}(N)$.
Several results have been achieved.
