PURPOSE: To maintain the constant tension to be exerted on a steel strip in the stage of cooling the steel strip, etc. with cooling rolls by correcting the number of revolutions of the cooling rolls after the moving roll on the uppermost stream in controlling the cooling rate with the movement of the moving rolls among the cooling rolls.

CONSTITUTION: A steel srip S having a high temp. is passed between stationary cooling rolls 1, 3, 5 and vertically movable rolls 2, 3 and is thereby cooled in the stage of cooling the strip S in a cooling zone 6 of a continuous heat treatment furnace. The temp. of the steel strip after cooling is measured with a thermometer 10 at the outlet of the zone 6 in this stage and the rolls 2, 4 are moved upward or downward according to the result thereof to change the contact area of the strip S with the rolls 1W5, thereby adjusting the cooling effect. The tension to be exerted on the strip S changes with the vertical movement of the rolls 2, 4 in this stage and therefore the change with time of the pass length L' (L0+L1+L2) of the steel strip between the adjacent rolls 1 and 2 is determined from the relation with the moving distance L of the roll 2 and the rotating speed of the rolls 2W5 is controlled, thereby maintaining the specified tension to be exerted on the steel strip and preventing the slackening and rupturing of the steel strip.