For the speed sensorless control of permanent magnet synchronous motor (PMSM), a design method based on model reference adaptive observer and single neuron PID speed loop was proposed. In this method, the model reference adaptive observer is used to identify the speed online, the Popov hyperstability is used to determine the reference adaptive law of the speed observer, the neural network module is used to control the q-axis current, and the LMS algorithm is selected to modify the weights of the neural network speed loop online. The simulation results show that the model reference adaptive speed observer control of PMSM based on single neuron PID is effective and robust.