PURPOSE: To accurately stop a rolling mill and to prevent the running through of a rolled stock by obtaining the data of current unwinding coil quantity from the current revolving speed of unwinding coil and the current revolving speed of a guide roll and comparing such data with the data of unwinding coil quantity at the start of deceleration.

CONSTITUTION: From the current revolving speed of the current unwinding coil 2 and that of the guide roll 3, the data of the current unwinding coil quantity is obtained which is indicated by the diameter, circumferential length, etc., of the unwinding coil 2. This data of the coil quantity and the remaining quantity of the unwinding coil at the start of the deceleration are compared; and when both are equal or the data of the current unwinding coil quantity becomes a smaller numeric value, the rolling mill is decelerated or stopped in accordance with a predetermined reduction ratio. During the deceleration, the unwinding coil 2 is rotated only by the quantity of an estimated coil transfer, the rolled stock of the predetermined remaining quantity is left on the spool 2a of the unwinding coil 2 in a coiled state, and the rolling mill is stopped.