Assume that $R$ is a commutative ring with nonzero identity. In this paper, we introduce and investigate { zero-annihilator graph of} $R$ denoted by $\mathtt{ZA}(R)$. It is the graph whose vertex set is the set of all nonzero nonunit elements of $R$ and two distinct vertices $x$ and $y$ are adjacent whenever ${\rm Ann}_R(x)\cap {\rm Ann}_R(y)=\{0\}$.