With the rise of industry 4.0 and the establishment of intelligent factories, how to use artificial intelligence algorithm to solve flexible job shop scheduling problem (FJSP) is one of the hot research. FJSP is proved to be a NP-hard problem with a large solution space. Compared with the job-shop scheduling problem (JSP), FJSP should not only know the processing time of the workpiece process, but also need the machine to optimize the objective function. Therefore, this paper considers the maximum completion time as the objective function, and proposes a deep reinforcement learning (DRL) algorithm to solve FJSP. Compared with heuristic rule and genetic algorithm, the numerical results show that DRL algorithm has better searching ability and better effect in solving FJSP problem, which provides a new idea for solving shop scheduling problem by artificial intelligence algorithm.