A motor speed control apparatus has a frequency generator for generating a frequency signal the frequency of which is proportional to the motor speed; a first pulse generator for producing a first pulse train having the same period as that of the frequency signal, each pulse of the first pulse train having a pulse width which is shorter than the period of the frequency signal and decreases as the frequency of the frequency signal increases; a second pulse generator for producing a second pulse train, the leading edges of the pulses of the second pulse train coinciding in timing with those of the first pulse train, each pulse of the second pulse train having a constant pulse width nearly the same as that of each pulse of the first pulse train obtained by the motor rotation at a predetermined speed; and a subtractor for producing a third pulse train by the subtraction of the pulses of the first pulse train and the corresponding pulses of the second pulse train, whereby there is produced a motor torque in correspondence with the third pulse train, and the motor speed can be controlled with suppressed motor vibration and excellent torque-speed characteristics of the motor.