A new method is proposed namely, multi-stage fuzzy binding (MFB) method for solving a constrained multi-stage machines flow-shop scheduling problem with different processing times and weights of jobs in fuzzy environment. The proposed method provides an optimal sequence to the given problem which is a non-crossing optimal sequence and minimizes the total fuzzy elapsed time. The procedure of the MFB method is illustrated with the help of numerical example. The proposed method helps the decision makers for finding an appropriate and applicable solution to constrained multi-stage machines flow-shop scheduling problems in real life situations. © Research India Publications.