A proper edge coloring of a graph G using the color set $$\{1,2,\ldots , k\}$${1,2,?,k} is called neighbor sum distinguishing if for any pair of adjacent vertices x and y the sum of colors taken on the edges incident to x is different from the sum of colors taken on the edges incident to y. The smallest value of k in such a coloring of G is denoted by $$\chi '_{_{\sum }}(G)$$???(G). In this paper, we show that $$\chi '_{_{\sum }}(G)\le 6$$???(G)≤6 for any simple subcubic graph G. This improves a result in Flandrin et al. (Graphs Combin 29:1329---1336, 2013), which says that every cubic graph G has $$\chi '_{_{\sum }}(G)\le 8$$???(G)≤8.