An apparatus for controlling the rotation speed of a motor, which is capable of controlling the rotation speed and the torque of the motor by detecting the input voltage and the input current of the motor without using a sensor for detecting the position of the rotor of the motor, is provided. The apparatus for controlling the rotation speed of a motor includes a synchronous/stationary coordinate converter for comparing the reference speed of a motor with the estimated speed of the motor and outputting reference magnetic flux component current and reference torque component current for compensating for an error value according to the comparison result as the reference voltage of an &agr; axis and the reference voltage of a &bgr; axis in a stationary coordinate system, a two phase current generator for receiving three phase current detected when the motor rotates and outputting magnetic flux component current and torque component current, a speed/position estimation operator for estimating the position and the rotation speed of a rotor in the motor on the basis of the reference of the &agr; axis, the reference voltage of the &bgr; axis, the current of the &agr; axis, the current of the &bgr; axis, and reference speed and controlling the rotation speed and the torque of the motor.