The annihilating-ideal graph of a commutative ring R with unity is deffned as the graph AG(R) whose 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. Nikan-dish et.al. proved that AG(Zn) is weakly perfect. In this short paper, we characterize n for which AG(Zn) is perfect.