A list assignment L of G is a mapping that assigns every vertex v∈ V (G) a set L (v) of positive integers. For a given list assignment L of G, an (L, r)-coloring of G is a proper coloring c such that for any vertex v with degree d (v), c (v)∈ L (v) and v is adjacent to at least min {d (v), r} different colors. The r-hued chromatic number of G, χ r (G), is the least integer k such that for any v∈ V (G) with L (v)={1, 2,…, k}, G has an (L, r)-coloring. The r-hued list chromatic number of G, χ L, r (G), is the least integer k such that for any v∈ V (G) and every list assignment L with| L (v)|= k, G has an (L, r)-coloring. Let K (r)= r+ 3 if 2≤ r≤ 3, and K (r)=⌊ 3 r/2⌋+ 1 if r≥ 4. We proved that if G is a K 4-minor free graph, then (i) χ r (G)≤ K (r), and the bound can be attained;(ii) χ L, r (G)≤ K (r)+ 1. This extends a former result in Lih et al.(2003).