In view of the chattering problem which was easily caused by traditional sliding mode control, a fuzzy radial basis function (RBF) neural network sliding mode observer was proposed to realize sensorless control of permanent magnet synchronous motor (PMSM). In order to reduce the chattering of the observer system, the fuzzy RBF neural network algorithm was used to adjust the sliding mode gain dynamically, and the stability of the observer was proved by Lyapunov stability theorem. The phase locked loop (PLL) technology was used to improve the estimation accuracy and reduce the computational noise. A simulation model was built based on the MATLAB/Simulink software platform, and the fuzzy RBF neural network sliding mode observer system was compared with the traditional sliding mode observer system. The results showed that, compared with the traditional sliding mode observer, the new type of sliding mode observer could track the rotor position rapidly and effectively, and accurately estimate the rotor speed, exhibiting good dynamic characteristics.