An adjacent vertex distinguishing proper edge coloring of a graph G is a proper edge coloring of G such that no pair of adjacent vertices meets the same set of colors. Let χ'a(G) be the minimum number of colors required to give G an adjacent vertex distinguishing proper edge coloring. In this paper, we show that χ'a(G) ≤ Δ(G) + 1 for bicyclic graphs G, where Δ(G) is the maximum degree of G.