  A star edge coloring of a graph $G$ is a proper edge coloring of $G$ such
that no path or cycle of length four is bi-colored. The star chromatic index of
$G$, denoted by $\chi^{\prime}_{s}(G)$, is the minimum $k$ such that $G$ admits
a star edge coloring with $k$ colors. Bezegov{\'a} et al. (Star edge coloring
of some classes of graphs, J. Graph Theory, 81(1), pp.73-82. 2016) conjectured
that the star chromatic index of outerplanar graphs with maximum degree
$\Delta$, is at most $\left\lfloor\frac{3\Delta}{2}\right\rfloor+1$. In this
paper, we prove this conjecture for a class of outerplanar graphs, namely
Cactus graphs, wherein every edge belongs to at most one cycle.
