In order to solve the inverse kinematics of manipulator with poor real-time performance and low precision, a particle swarm optimization (PSO) algorithm for LSTM was proposed in this paper.Firstly, the model of the series 6-DOF manipulator is established for kinematic analysis, and the training data are obtained. Next, Optimizing the quantity of hidden level neural units and learning percentage of the long-term and short-term memory network by PSO. LSTM after parameter optimization learns the mapping relationship between the position and pose of the manipulator's end effector and joint variables. Finally, the trained PSO-LSTM model is used to predict the joint variables of the manipulator to obtain the inverse kinematics solution. The experimental results show that the inverse kinematics solution speed of the model is kept within 10 ms, which is tens of times higher than that of the traditional solution, and the mean square error of the model is as low as 0.001, which can not only improve the solution speed but also ensure the solution accuracy.