In this paper, we mix both concepts of s-Godunova-Levin and m-convexity and introduce the (s,m)-Godunova-Levin functions. We introduce the fuzzy Hermite-Hadamard inequality for (s,m)-Godunova-Levin functions via fractional integral. Holder inequality is used for new bounds for fuzzy Hermite-Hadamard inequality. Then we accommodate this result with the previous works that have been done before. c 2016 All rights reserved.