  Proper edge coloring of a graph $G$ is called acyclic if there is no
bichromatic cycle in $G$. The acyclic chromatic index of $G$, denoted by
$\chi'_a(G)$, is the least number of colors $k$ such that $G$ has an acyclic
edge $k$-coloring. Basavaraju et al. [Acyclic edge-coloring of planar graphs,
SIAM J. Discrete Math. 25 (2) (2011), 463--478] showed that $\chi'_a(G)\le
\Delta(G)+12$ for planar graphs $G$ with maximum degree $\Delta(G)$. In this
paper, the bound is improved to $\Delta(G)+10$.
