Under a method to control a sliding speed in accordance with this invention, the motor is initially accelerated for a predetermined reference speed, and then during the initial acceleration period, if a rotational speed of the wire drum is of and above a given value, a difference between a rotational speed of the wire drum and a rotational speed of the motor is of and above a given value, and a rate of acceleration of the wire drum is of and above a given value, the rotational speed of the motor is reduced temporarily judging the slide door is in a state of abnormal acceleration, and then the motor is accelerated again at a lower rate than the initial acceleration toward the reference speed.