Giving a planar graph G, let χ'_l(G) and χ''_l(G) denote the list edge chromatic number and list total chromatic number of G respectively. It is proved that if G is a planar graph without non-induced 7-cycles, then χ'_l(G)≤Δ(G)+1 and χ''_l(G)≤Δ(G)+2 where Δ(G)≥7.