PROBLEM TO BE SOLVED: To decelerate and stop a rolling mill so that the end of a rolled bar stock is not thrusted through the reel on the delivery side by correcting the speed of the bar stock on the inlet side to a value close to the actual value even when an error is produced in the speed of the bar stock on the inlet side due to a slip or the like between the rolled bar stock and guide rollers. SOLUTION: Delivered length L after starting deceleration of the rolling mill to stopping is compared with the remaining length L' which is left on the pay-off reel and the deceleration of the rolling mill is started so that the rolled bar stock is left on the pay-off reel when the rolling mill is stopped, but, when there is no error in the speed VB of the bar stock on the inlet side detected from the circumferential speed of the guide roller on the inlet side, the delivered length L of the bar stock is determined from the measured value of the speed VB of the bar stock on the inlet side, measured value of the circumferential speed VM of a rolling roll and speed reduction ratio α of the rolling roll. When the error is produced in the speed VB of the bar stock on the inlet side, the error is produced in the calculation of the delivered length, so the proximate speed VB' of the bar stock on the inlet side is determined from the circumferential speed VM of the rolling roll, the measured value of the thickness tB on the inlet side and the thickness tF on the outlet side of the rolled bar stock and estimated forward slip λF preliminarily inputted by VB'=VM.(1+λF).tF/tB and the delivered length L of the bar stock is determined from this proximate speed VB of the bar stock on the inlet side, circumferential speed VM of the rolling roll and speed reduction ratio α.