Abstract: Hot steel plate as hot-rolled is passed forward longitudinally through pairs of top and bottom rollers disposed in the direction of the plate travel. The steel plate is cooled with water supplied to its top and bottom surfaces from the nozzles on a plurality of cooling units disposed in the same longitudinal direction. Each cooling unit is disposed between adjoining pairs of the top and bottom rollers. Before cooling is started, the temperature distribution in the steel plate is determined and the desired mean cooling rate is set. The distance from the plate edge over which the supply of the cooling water at least to the bottom side of the plate is to be cut off is determined for each cooling unit on the basis of the determined temperature distribution and preset mean cooling rate. By so doing, the temperature of the inner edge portion of the steel plate is kept above the temperature of the middle portion, thereby allowing the Ar.sub.