  {\emph A star edge-coloring} of a graph is a proper edge-coloring without
bichromatic paths and cycles of length four. In this paper, we consider the
list version of this coloring and prove that the list star chromatic index of
every subcubic graph is at most $7$, answering the question of Dvo\v{r}\'{a}k
et al. (Star chromatic index, J. Graph Theory 72 (2013), 313--326).
