  A star edge coloring of a graph $G$ is a proper edge coloring of $G$ such
that every path and cycle of length four in $G$ uses at least three different
colors. The star chromatic index of $G$, is the smallest integer $k$ for which
$G$ admits a star edge coloring with $k$ colors.
  In this paper, we obtain tight upper bound
$\left\lfloor\frac{3\Delta}{2}\right\rfloor+2$ for the star chromatic index of
every Halin graph, that proves the conjecture of Dvo{\v{r}}{\'a}k et al. (J
Graph Theory, 72 (2013), 313--326) for cubic Halin graphs.
