A graph is IC-planar if it admits a drawing in the plane such that each edge is crossed at most once and two crossed edges share no common end-vertex.A proper total-k-coloring of G is called neighbor sum distinguishing if ∑c(u) ≠ ∑c(v) for each edge uv ∈ E(G),where ∑c(v) denote the sum of the color of a vertex v and the colors of edges incident with v.The least number k needed for such a total coloring of G,denoted by X∑(G),is the neighbor sum distinguishing total chromatic number.Pil(s)niak and Wo(z)niak conjectured X∑(G) ≤ △(G) + 3 for any simple graph with maximum degree △(G).By using the famous Combinatorial Nullstellensatz,we prove that above conjecture holds for any triangle free IC-planar graph with △(G) ≥ 7.Moreover,it holds for any triangle free planar graph with △(G) ≥ 6.