  The annihilating-ideal graph of a commutative ring $R$ with unity is defined
as the graph $\mathbb{AG}(R)$ with the vertex set is the set of all non-zero
ideals with non-zero annihilators and two distinct vertices $I$ and $J$ are
adjacent if and only if $IJ = 0$. Nikandish {\it et.al.} proved that
$\mathbb{AG}(\mathbb{Z}_n)$ is weakly perfect. In this short paper, we
characterize $n$ for which $\mathbb{AG}(\mathbb{Z}_n)$ is perfect.
