  Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative
ring and $M$ a graded $R$-module. A proper graded submodule $Q$ of $M$ is
called a graded quasi-primary submodule if whenever $r\in h(R)$ and $m\in h(M)$
with $rm\in Q$, then either $r\in Gr((Q:_{R}M))$ or $m\in Gr_{M}(Q)$. The
graded quasi primary spectrum $qp.Spec_{g}(M)$ is defined to be the set of all
graded quasi primary submodules of $M$. In this paper, we introduce and study a
topology on $qp.Spec_{g}(M)$, called the Quasi-Zariski Topology, and
investigate properties of this topology and some conditions under which (%
$qp.Spec_{g}(M)$, $q.\tau ^{g}$) is a Noetherian, spctral space.
