Let p and q be two positive integers with p≥q, and let λ_{p,q}(G) be the L(p,q)-labeling number of a planar graph G. It is proved that λ_{p,q}(G)≤(2q-1)Δ(G)+6p+10q-8 if G is a planar graphs with girth g(G)≥5, which implies Wegner’s conjecture holds for a planar graph G with girth g(G)≥5 and Δ(G)≥16.