A speed control apparatus for a rotary motor includes a motor for rotating at a speed based on a torque command and which outputs a present angular position and a present angular speed of the motor. A speed measuring unit is provided for obtaining a speed error representing the difference between a reference angular speed and a present angular speed. A speed controller is provided for outputting a current command for controlling a rotational speed of the motor. A learning compensator is provided for correcting an effect of a disturbance expressed as a function of an angular position and an angular speed applied to the motor, via a repetitive learning process using the reference angular speed, any one of the speed error from the speed measuring unit and the current command output from the speed controller and the present angular position of the motor, for removing a high frequency noise generated in the repetitive learning process, and for outputting a resultant disturbance correction value. A speed command compensator is provided for obtaining a corrected current command by adding the current command value output from the speed controller and the disturbance correction value obtained in the learning compensator; and a current controller is provided for receiving the corrected current command and outputting a torque command to the motor. Thus, the apparatus stores in advance the correction value obtained in the learning compensator and effectively performs a speed control using the stored value.