The poor robustness of permanent magnet synchronous motor (PMSM) is caused by constant sliding mode gain when the traditional super twisting algorithm second order sliding mode observer (STASSMO) is used to estimate the rotor position and speed. For this problem, a fuzzy super twisting algorithm second order sliding mode observer (FSTASSMO) is proposed under the existing stable conditions. The fuzzy controller is used to set the sliding mode gain according to the fuzzy rules. The sliding mode gain self tuning process of the super-twisting algorithm (STA) is realized, which improves the observation accuracy, broadens the effective observation range, and enhances the robustness of position sensorless vector control system of PMSM. Finally, the proposed algorithm is verified by a simulation control system built in MATLAB circumstances. The simulation result shows that the proposed algorithm is effective.