A Hybrid Adaptive Mutation Particle Swarm Optimization algorithm is proposed for the Job Shop scheduling problem. In the process of running, the mutation probability for the current best particle is determined by two factors: the variance of the population's fitness and the current optimal solution. Through combining genetic algorithms and simulated annealing algorithms with the Adaptive Mutation PSO algorithm, numerical simulation demonstrates that within the framework of the newly designed hybrid algorithm, the NPhard classic job shop scheduling problem can be solved efficiently.