A proper [k]-edge coloring of a graph G is a proper edge coloring of G using colors from $$[k]=\{1,2,\ldots ,k\}$$ [ k ] = { 1 , 2 , … , k } . A neighbor sum distinguishing [k]-edge coloring of G is a proper [k]-edge coloring of G such that for each edge $$uv\in E(G)$$ u v ∈ E ( G ) , the sum of colors taken on the edges incident to u is different from the sum of colors taken on the edges incident to v. By nsdi(G), we denote the smallest value k in such a coloring of G. It was conjectured by Flandrin et al. that if G is a connected graph with at least three vertices and $$G\ne C_5$$ G ≠ C 5 , then nsdi $$(G)\le \varDelta (G)+2$$ ( G ) ≤ Δ ( G ) + 2 . In this paper, we prove that this conjecture holds for $$K_4$$ K 4 -minor free graphs, moreover if $$\varDelta (G)\ge 5$$ Δ ( G ) ≥ 5 , we show that nsdi $$(G)\le \varDelta (G)+1$$ ( G ) ≤ Δ ( G ) + 1 . The bound $$\varDelta (G)+1$$ Δ ( G ) + 1 is sharp.