In order to realize the sensorless control of PMSM (permanent magnet synchronous motor), an error-corrected LSTM(long short-term memory) speed observation model was proposed. The model combined the LSTM neural network with the motor mathematical model. The difference between the actual value of the motor speed and the calculated value of the mathematical model(the error calculated by the mathematical model) was trained as the output of the neural network, and the real-time observation of the motor speed was realized. The model was applied to the PMSM vector control system to simulate the load torque and given speed change of the motor under different operating conditions, and was compared with the neural network observation model which directly trained the motor speed as output. The results show that the training burden of neural network based on speed error training is less and the speed observation is more accurate. In addition, combined with the characteristics of the motor system, the neural network model was improved to optimize the accuracy of speed observation further. The simulation results show that the speed observation error of the improved model is smaller, the speed observation accuracy is 99.084%, and the motor system runs stably, which verifies the effectiveness and superiority of the method.