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 $��_i(G)$. In this paper, the injective chromatic number of outerplanar graphs with maximum degree $��$ and girth $g$ is studied. It is shown that for every outerplanar graph, $��_i(G)\leq ��+2$, and this bound is tight. Then, it is proved that for outerplanar graphs with $��=3$, $��_i(G)\leq ��+1$ 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 $��=3$, $g\geq 6$ and $��\geq 4$, $g\geq 4$ is equal to $��$.

13 pages, 6 figures