The mathematical model of flexible job-shop scheduling problem is established to minimize the maximum completion time of all workpieces under the constraints of processing sequence and processing time. A three population co-evolution algorithm was proposed to solve the model. Based on the three-way tournament method, the population was divided into superior, medium and inferior subpopulations, and the corresponding search strategy was designed according to the individual characteristics of different subpopulations. The superior subpopulation uses load balance and variable neighborhood descent local search of critical path to improve the solution accuracy and excavate better solutions. In the medium subpopulation, adaptive Jaya operation was used to avoid the bad in the early stage of evolution, and the maintenance of population diversity was emphasized in the middle and late stages. Multiple cross global search was adopted for inferior subpopulation, and the crossover operators that could generate viable individuals were designed for different gene strings. At the same time, individuals in other subpopulations were taken as crossover objects to strengthen the cooperative interaction among subpopulations. A large number of experimental results in standard test examples and production instances show that the proposed algorithm has significantly better performance than the representative algorithm in most cases.