  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 $\Delta(G)$. A graph is {\em
$1$-planar} if it can be drawn on the plane such that every edge is crossed by
at most one other edge. In this paper, we prove that every triangle-free
$1$-planar graph $G$ has an acyclic edge coloring with $\Delta(G) + 16$ colors.
