A　proper　edge　coloring　of　a　graph　G　is　called　acyclic　if　there　is　no　2-colored　cycle　in　G.　The　acyclic　edge　chromatic　number　of　G,　denoted　by　a＇(G),　is　the　least　number　of　colors　in　an　acyclic　edge　coloring　of　G.　Alon　et　al.　conjectured　that　a＇(G)　acurrency　sign　Delta(G)　+　2　for　any　graphs.　In　this　paper,　it　is　shown　that　the　conjecture　holds　for　planar　graphs　without　4-　and　5-cycles　or　without　4-　and　6-cycles.