Let $R$ be a commutative ring with identity and $\mathbb{A}(R)$ be the set of ideals with nonzero annihilator. The annihilating-ideal graph of $R$ is defined as the graph $\mathbb{AG}(R)$ with the vertex set $\mathbb{A}(R)^{*}=\mathbb{A}(R)\smallsetminus\{0\}$ and two distinct vertices $I$ and $J$ are adjacent if and only if $IJ=0$. In this paper, we study the domination number of $\mathbb{AG}(R)$ and some connections between the domination numbers of annihilating-ideal graphs and zero-divisor graphs are given.