An elevator car and a counterweight is suspended on a sheave by means of a rope in a well-rope faashion. In dependence on the number of passengers on the car, the sheave is applied with an unbalance torque making appearance between the car and counterweight. Upon starting of the elevator operation by releasing a brake, upward or backward bouncing of the car takes place due to the unbalance torque. For preventing such bouncing of the car, a start compensation is performed by generating a motor torque which can cancel out the unbalance torque in precedence to the releasing of the brake. The brake is installed swingably on a winding equipment. Displacement of the brake during actuation thereof indicates the presence of the unbalance torque. By taking advantage of this displacement, the start compensation is carried out by increasing the motor torque progressively in the direction depending on the displacement and by holding the motor torque constant at a value attained when the displacement becomes smaller than a predetermined value.