Let

$S$ be a commutative multiplicative semigroup with 0 (

$0x=0$ for all

$x\in S$). In this paper, the authors introduce and investigate the zero-divisor graph of

$S$, denoted by

${\Gamma}\left(S\right)$. In analogy with the recently studied zero-divisor graph of a commutative ring, the vertices of

${\Gamma}\left(S\right)$ are the nonzero zero-divisors of

$S$, and two distinct vertices

$x$ and

$y$ are connected by an edge if

$xy=0$. They give several results about the shape of

${\Gamma}\left(S\right)$. For example,

${\Gamma}\left(S\right)$ is always connected and the diameter of

${\Gamma}\left(S\right)\le 3$. The graphs without a cycle which can be realized by some

${\Gamma}\left(S\right)$ are determined. If

${\Gamma}\left(S\right)$ contains a cycle, then the core of

${\Gamma}\left(S\right)$ is a union of squares and triangles, and any vertex not in the core is an end which is connected to the core by a single edge.