To provide a damping device with which a steel plate is correctly controlled even when the end of the steel plate is put in a half-way position between a pair of electromagnets.

One channel has the electromagnets 1 with which magnetic force is applied to the surface or the back surface of the steel plate 4, a displacement sensor 2 detecting the displacement in the distance between the electromagnets and the steel plate and a presence sensor 3 detecting the presence or nonpresence of the steel plate, a plurality of the channels are arranged in the width direction crossing the running direction of the steel plate and this device has control means with which, provided that the presence of the steel plate is detected with the presence sensor of each channel, the electromagnets of the channel in which this presence sensor is included are turned on and, based on the displacement detected with the displacement sensor of each channel, the amount of an exciting current which is made to flow through the electromagnets of the channel including this displacement sensor is controlled and the position of the presence sensor in the width direction of the steel plate is taken as the same position as the boundary position of a range 2a which is necessary for the displacement sensor to detect the displacement or the outside of the boundary position.