Steel hot-rolled to the desired diameter and allowed to travel forward is quenched with cooling water to a temperature below the bainite transformation temperature chosen from within the following range:145.multidot.t/r.sup.2 +130.ltoreq.T.ltoreq.152.multidot.t/r.sup.2 +240whereT=surface temperature of the rolled steel at a point 1 m to 2 m away form the point where quenching ends (.degree.C.)t=time required by the rolled steel for travelling from the quenching ending point to the temperature measuring point (hr)r=radius of the rolled steel (m).Then, the surface area of the rolled steel is subsequently automatically recovered by the heat of the core.