This article proposes a novel differential evolution algorithm based on dynamic multi-population (DEDMP) for solving the multi-objective flexible job shop scheduling problem. In DEDMP, at each generation, the whole population is divided into several subpopulations by the clustering partition and the size of the subpopulation is dynamically adjusted based on the last search experience. Furthermore, DEDMP is adaptive based on two search strategies, one with strong exploration ability and the other with strong exploitation ability. The selection probability of each search strategy is also dynamically adjusted according to the success rate. Furthermore, the proposed algorithm adopts newly designed mutation and crossover operators and it can directly generate feasible solutions in the search space. To evaluate the performance of DEDMP, DEDMP is compared with some state-of-the-art algorithms on benchmark instances. The experimental results show that DEDMP is better than or at least competitive with other outstanding algorithms.