A 2-distance k-coloring of a graph G is a proper k-coloring such that any two vertices at distance two get different colors. $$\chi _{2}(G)$$ χ2(G) =min{k|G has a 2-distance k-coloring}. Wegner conjectured that for each planar graph G with maximum degree $$\Delta $$ Δ , $$\chi _2(G) \le 7$$ χ2(G)≤7 if $$\Delta \le 3$$ Δ≤3 , $$\chi _2(G) \le \Delta +5$$ χ2(G)≤Δ+5 if $$4\le \Delta \le 7$$ 4≤Δ≤7 and $$\chi _2(G) \le \lfloor \frac{3\Delta }{2}\rfloor +1$$ χ2(G)≤⌊3Δ2⌋+1 if $$\Delta \ge 8$$ Δ≥8 . In this paper, we prove that: (1) If G is a planar graph with maximum degree $$\Delta \le 5$$ Δ≤5 , then $$\chi _{2}(G)\le 20$$ χ2(G)≤20 ; (2) If G is a planar graph with maximum degree $$\Delta \ge 6$$ Δ≥6 , then $$\chi _{2}(G)\le 5\Delta -7$$ χ2(G)≤5Δ-7 .