In this paper, a memetic non-dominated sorting particle swarm optimization algorithm is proposed for the discrete flexible job shop scheduling. Shorting the production period, reducing the machine idle time and improving the product qualification rate are the algorithm's optimization objectives. This algorithm adopts two-dimensional coding method. First, a multi-objective discrete resources optimization scheduling model is established by different mutation operation for the process and the machine allocation. Then, the Pareto optimal solution is obtained using the non-dominated sorting strategy and the random walk method. Besides, using the analytic hierarchy method, the resource optimal allocation scheme is given. Finally, the actual production data is used for simulation. The result shows that the proposed optimization algorithm can balance the global search and the local exploitation abilities.