  For a vertex $x$ of a graph $G$, let $N_G[x]$ be the set of $x$ with all of
its neighbors in $G$. A set $C$ of vertices is an {\em identifying code} of $G$
if the sets $N_G[x]\cap C$ are nonempty and distinct for all vertices $x$. If
$G$ admits an identifying code, we say that $G$ is identifiable and denote by
$\gamma^{ID}(G)$ the minimum cardinality of an identifying code of $G$. In this
paper, we study the identifying code of the corona product $H\odot G$ of graphs
$H$ and $G$. We first give a necessary and sufficient condition for the
identifiable corona product $H\odot G$, and then express $\gamma^{ID}(H\odot
G)$ in terms of $\gamma^{ID}(G)$ and the (total) domination number of $H$.
Finally, we compute $\gamma^{ID}(H\odot G)$ for some special graphs $G$.
