PURPOSE: To improve the quality and yield of a billet by calculating the moving time and angle of temp. detectors embedded in a water-cooled roll and controlling the circumferential speed of the water-cooled roll.

CONSTITUTION: Temp. detectors 10 are embedded at a suitable interval on the same circumference in proximity to the outside circumference of one roll of a pair of water- cooled rolls 1, 1' rotating synchronously in opposite directions. Pulses signals are respectively transmitted at the time when the detector 10 passes the position having a reference angle θ0 with a reference line X by rotation of the roll 1 and the angle at which the temp. of a molten steel 3 is detected after passage through the reference position θ0. The required time between the two pulse signals is determined. The time required for the roll 1 to contact first with the steel 3 from the position θ0 and the position thereof are determined according to said time. The circumferential speed of the rolls 1, 1' is so controlled that the differnece in the angle between the point if the first contact of the roll 1 with the steel 3 and the reference line and the required set angle with respect to the reference line X is made zero. The molten steel surface between the rolls 1, 1' and side dams is thus maintained at the set level.