To raise the line speed to a target speed without developing roll slipping, etc., even in the case of thermally deforming the roll by repeating the accelerating operation by a prescribed quantity to the speed in a furnace when the periodical tension variation quantity of a steel strip becomes a thresfold or lower.

In a heat treatment furnace of a continuous heat treatment line for applying the heat treatment to a steel strip, the periodical tension variation quantity is calculated from an actual value of the steel strip tension just after starting the operation of the line. This tension variation quantity is reduced according as reducing of the thermal deformation of the roll in the furnace, and at the stage becoming a first thresfold or lower, the steel strip speed in the furnace is accelerated by the prescribed quantity until the tension variation quantity exceeds a second thresfold, and when the steel strip speed exceeds the second thresfold, the accelerating operation of this speed in the furnace is stopped. Successively, at the stage when the tension variation quantity becomes the second thresfold or lower, the acceleration of the speed in the furnace is again executed, and this operation is repeated until the speed in the furnace becomes the target speed. In this way, the acceleration of the line speed is executed without developing the roll slipping and backling.