  A star edge coloring of a graph $G$ is a proper edge coloring of $G$ without
bichromatic paths or cycles of length four. The it star chromatic index,
$\chi_{st}^{'} (G ),$ of $G$ is the minimum number $k$ for which $G$ has a star
edge coloring by $k$ colors. In \cite{LB},
  L. Bezegov$\acute{a}$ et al. conjectured that $\chi_{st}^{'} (G )\leq
\lfloor\frac{3\Delta}{2}\rfloor+1$ when $G$ is an outerplanar graph with
  maximum degree $\Delta \geq 3.$ In this paper we obtained that
$\chi_{st}^{'}(G) \leq \Delta+6$ when $G$ is an 2-connected outerplanar graph
with diameter 2 or 3. If $G$ is an 2-connected outerplanar graph with maximum
degree 5, then $\chi_{st}^{'}(G) \leq 9.$
