The invention discloses a method and a device for controlling speed of a permanent-magnet synchronous motor. The method includes that an active-disturbance-rejection control technology is adopted for a speed ring, speed setting and a speed detection value are taken as input of a first-order active-disturbance-rejection controller, a tracking differentiator reasonably arranges a transition process, an extended state observer observes an actual value of rotating speed of the motor, estimates total disturbance of a system and acquires output of the speed ring through a nonlinear state error feedback control ratio, a load torque observer is designed through detection values of a current and the speed, and observed load torque through output of a feedforward controller and the active-disturbance-rejection controller is taken as reference input of a quadrature-axis current. The method carries forward characteristics of overshoot freeness, high disturbance rejection capacity, good robustness and the like of the permanent-magnet synchronous motor in speed control in the active-disturbance-rejection control technology, and compensation is performed on the problem of load disturbance, so that the problem of fluctuation of the rotating speed under the circumstance of load disturbance is improved.