  An acyclic edge coloring of a graph $G$ is a proper edge coloring such that
every cycle is colored with at least three colors. The acyclic chromatic index
$\chiup_{a}'(G)$ of a graph $G$ is the least number of colors in an acyclic
edge coloring of $G$. It was conjectured that $\chiup'_{a}(G)\leq \Delta(G) +
2$ for any simple graph $G$ with maximum degree $\Delta(G)$. In this paper, we
prove that every planar graph $G$ admits an acyclic edge coloring with
$\Delta(G) + 6$ colors.
