Two distinct crossings are independent if the end-vertices of any two pairs of crossing edges are disjoint. If a graph G has a drawing in the plane such that every two crossings are independent, then we call G a plane graph with independent crossings or IC-planar graph for short. A proper edge coloring of a graph G is acyclic if there is no 2-colored cycle in G. The acyclic chromatic index of G is the least number of colors such that G has an acyclic edge coloring and denoted by χ a (G). In this paper, we prove that χ a (G) ≤ ∆(G)+17, for any IC-planar graph G with maximum degree ∆(G).