The invention relates to a method of controlling the speed of a super-speed permanent magnet synchronous motor based on an ARC (Adaptive Robust Controller). The design of an ARC includes the steps as follows: building a mathematical model of a motor, converting the model into a state equation, and making relevant assumptions; designing a motor speed loop, a torque loop and a flux loop, and calculating the voltage control quantity; and applying the voltage control quantity to an SVPWM (Space Vector Pulse Width Modulation) module to control the speed of the motor. The robustness and control precision of a motor system are improved. The speed of a super-speed permanent magnet synchronous motor can be controlled stably and reliably.