PURPOSE: To guarantee passage of rolled stock having less longitudinal tensile strength economically and rationally by driving only the hydromotor of one of the rolling stands until the completion of biting or passing through all rolling stands, for the purpose of controlling the rotary speeds.

CONSTITUTION: At the beginning of rolling, during the passing of rolling stands 1, 2, 3, all but one of the rotary speed controls for the hydromotors 5 belonging to the stand 1 through which a stock W has passed and the stand 2, through which the stock passes next are consecutively interrupted in accordance with the extent of the consecutive passing. Therefore, only the hydromotor of this one stand, as the guiding stand, is operated for controlling the rotary speed with an adjustable displacement volume as long as the stock passes through all the stands 1, 2, 3. As a result, a costing arithmetic unit or the like can be dispensed with.