The Fuzzy Job-Shop Scheduling Problems (FJJSP) are NP-hard and several meta-heuristic optimization algorithms were considered to solve them. Since there are human errors and the possibility of system failure, the due date of each job cannot be crisp. So, the FJSSP with fuzzy due date created to consider the real-world realities. In this paper, two objects such as minimizing the maximum of the makespan and maximizing the minimum of the satisfaction degree are considered to solve the FJSSP with fuzzy due date. To achieve to this aim, a modified draft of multi-objective particle swarm optimization (MOPSO) are designed to obtain the optimal Pareto solutions. A technical preprocessing and dynamic management repository of non-dominated solutions are proposed to enhance the MOPSO. The comparison of the experimental results, based on a set of benchmark datasets, with the results of the non-dominated sorting genetic algorithm (NSGA-II) proves the advantages.