Abstract For flexible job shop scheduling, an improved migratory bird migration algorithm is proposed to minimize the maximum completion time. Firstly, global, local and random selection methods were used to initialize the population, which improved the quality of the initial solution; The structure of migratory bird group was changed by increasing leading birds, and the crossover and mutation operators were introduced to enhance the global optimization ability. And different variable neighborhood search algorithms on critical path were introduced among different bird groups, which improved the local optimization ability of and the diversity of migratory bird groups; The jumping and competition mechanisms were proposed to improve the ability of the algorithm to jump out of the local optimal solution and convergence. Finally, the simulation results of the benchmarks verified the algorithm’s searching ability and stability of the algorithm.