  Let $G$ be a group with identity $e$ and $R$ be a $G$-graded commutative ring
with nonzero unity $1$. In this article, we introduce the concept of graded
strongly $1$-absorbing primary ideals. A proper graded ideal $P$ of $R$ is said
to be a graded strongly $1$-absorbing primary ideal of $R$ if whenever nonunit
homogeneous elements $x, y, z\in R$ such that $xyz\in P$, then either $xy\in P$
or $z\in Grad(\{0\})$ (the graded radical of $\{0\}$). Several properties of
graded strongly $1$-absorbing primary ideals are investigated. Many results are
given to disclose the relations between this new concept and others that
already exist. Namely, the graded prime ideals, the graded primary ideals, and
the graded $1$-absorbing primary ideals.
