In this paper, we consider the Minimum Maximal Network Flow Problem (MMNFP), i.e., minimizing the flow value, minimizing the total time among the maximal flow with time-windows, which is a combinatorial optimization and an NP-hard problem. We propose a new version of a MMNFP, this version is a Minimum Maximal Network Fuzzy Flow Problem with Fuzzy Time-Windows (MMNFFPFTW). After a mathematical modeling problem, we introduce some formulations of the problem and one of them is minimization of the concave function over a fuzzy convex set. The problem can also be cast into a difference of the convex (nonconvex) functions programming. We propose a new algorithm of the MMNFFPFTW.