PURPOSE: To prevent the meandering of a rolling stock while stably correcting the amount of off-center by detecting the difference between the amount of off-center and rolling reduction of a rolling stock and adjusting the difference in rolling reduction by using both detected values.

CONSTITUTION: Rolling-load detectors 20, 22 are provided to both ends of a lower backup roll 18, and their outputs are inputted to an adder 24 and a subtractor 26 respectively. The adder 24 outputs the load sum of rolling rolls at the driving and operating sides and the subtractor 26 outputs the load difference between them, to an arithmetic and control unit 28. On the other hand, rolling reduction devices 30, 32 with rolling-reduction detectors are provided to both ends of an upper backup roll 18, and the outputs of them are inputted to an subtractor 34. The difference in rolling reduction between both ends of an upper backup roll 16 i.e. the amount of leveling is outputted to the unit 28 to operate the amount of off-center as well as to estimate the internal variables of meandering phenomenon, and the sum of the estimated value and the amount of off-center multiplied respectively by a gain i.e. the changing amount of leveling is operated to output the results to the devices 30, 32 in order to correct the amount of off-center.