An apparatus for controlling a speed of a motor, includes: a first duty change detection unit detecting a change in duty of a PWM signal supplied from the outside; a speed conversion unit converting a speed indication (command) having the PWM signal into an actual speed value (RPM value) based on the change in duty detected by the first duty change detection unit; a speed control unit generating a new speed indication value to be applied to a motor and determining the duty value of PWM signal based on the new speed indication value; a second duty change detection unit detecting the change in the duty value of PWM signal determined by the speed control unit; and a PWM generation unit generating the PWM signal actually applied to the motor based on the change in the duty value detected by the second duty change detection unit.