  Let $G$ be a group, $R$ be a $G$-graded commutative ring with nonzero unity
and $GI(R)$ be the set of all graded ideals of $R$. Suppose that
$\phi:GI(R)\rightarrow GI(R)\cup\{\emptyset\}$ is a function. In this article,
we introduce and study the concept of graded $\phi$-$1$-absorbing prime ideals.
A proper graded ideal $I$ of $R$ is called a graded $\phi$% -$1$-absorbing
prime ideal of $R$ if whenever $a,b,c$ are homogeneous nonunit elements of $R$
such that $abc\in I-\phi(I)$, then $ab\in I$ or $c\in I$. Several properties of
graded $\phi$-$1$-absorbing prime ideals have been examined.
