For the job shop scheduling problem with fuzzy processing time and fuzzy delivery time, this paper uses the proximal policy optimization(PPO) algorithm as the basic optimization framework with the objective of minimizing the maximum completion time. An LSTM-PPO(proximal policy optimization with long short-term memory) algorithm is proposed to solve the problem. Firstly, a new state feature is designed to model the scheduling problem, and the process is selected directly based on the modeled state feature, which is closer to the actual scheduling decision process. Them, the long short-term memory(LSTM) network is applied to the actor-commentator framework of the PPO algorithm, which solves the problem that the traditional model is difficult to scale up when the problem size changes, and enables the intelligent body to obtain the final scheduling solution even when the number of workpieces, processes, and machines changes. On the selected problem set of fuzzy job shop scheduling, it is experimentally verified that the algorithm can achieve better performance.