PURPOSE: To remove the tension applying to the welded part and to prevent the tube from breaking or shape being bad by reducing the speed of the downstream stand at the timing that the position of the welded part of pipe reaches just under the stand, and eliminating the difference of speed between the stands.

CONSTITUTION: The tube 2 as the material to be rolled is passed to each stand 1 of the stretch reducer mill and rolled. On this time, the speed compensation starting timing of each stand 1 is decided by trucking the part to be welded 3 with the distance between the top of tube before rolling and the welded part 3, the elongated length of tube 2, the roll diameter of each stand 1, the detected signal of tube top at the inlet and each roll speed signal as the input with the compensation start timing setting device 12. Further, the compensating quantity computing element 14 operates the speed reducing quantity of the downstream stand to be corrected at reaching time to the each stand 1 so that the tension is not applied to the welded part 3 of the tube. Therefore, the tension applied to the welded part 3 is reduced by reducing the speed of the downstream at the timing that the welded part 3 of the tube reaches just under the stand, and eliminating the speed difference between the stands where the welded part 3 exists.