In order to solve parameter fluctuations and disturbances, a novel fractional order model reference adaptive speed observer that estimates the rotor position and the angular velocity from the stator currents is proposed for sensorless control of permanent-magnet synchronous motors (PMSM). Firstly, a novel fractional order model reference adaptive controller (FOMRAC) for adaptive identification is designed to achieve fast response and high precise identification of load torque in the full speed range when the motor is running at variable-speed or variable-load. Additionally, an appropriate adjustable matrix P is chosen to make the convergence of the adaptive law meet the requirements. Next, an improved model reference adaptive observer (MRAO) is proposed to suppress the serious chattering and compensate rotor position error, which can stabilize the system. The validity of the proposed fractional order model reference adaptive sensorless control strategy for PMSM is demonstrated with simulations.