  An injective coloring of a graph is a vertex coloring where two vertices with
common neighbor receive distinct colors. The minimum integer $k$ that $G$ has a
$k-$injective coloring is called injective chromatic number of $G$ and denoted
by $\chi_i(G)$. In this paper, the injective chromatic number of outerplanar
graphs with maximum degree $\Delta$ and girth $g$ is studied. It is shown that
for every outerplanar graph, $\chi_i(G)\leq \Delta+2$, and this bound is tight.
Then, it is proved that for outerplanar graphs with $\Delta=3$, $\chi_i(G)\leq
\Delta+1$ and the bound is tight for outerplanar graphs of girth three and $4$.
Finally, it is proved that, the injective chromatic number of $2-$connected
outerplanar graphs with $\Delta=3$, $g\geq 6$ and $\Delta\geq 4$, $g\geq 4$ is
equal to $\Delta$.
