The job shop scheduling problem with the shortest maximum completion time is studied, and the current research status for the solution of the job shop scheduling problem is reviewed. A hybrid algorithm combining flower pollination algorithm with genetic algorithm is proposed. Based on the flower pollination algorithm, the iterative formula of global search and local search are redefined, and the selection, priority crossover and mutation operations of genetic algorithm are integrated into the assimilation operation, so as to further enhance the exploration ability of the proposed algorithm. Numerical testing on the 26 classic benchmark scheduling problems and comparison with other algorithms in recent 5 years show the proposed algorithm's advantages in solving job-shop scheduling problems.