PURPOSE: To prevent the occurrence of roll flaws then the strip tip and rear end bite into rolling rolls without grinding burrs.

CONSTITUTION: The annealing device for the strip tip and rear end is composed of tip and rear end detectors 3 of a strip 2 arranged on the inlet side of a rolling mill 1, a heating device 5 having a strip clamping device and consisting of a heating burner freely movable in the traveling direction of the strip between the tip and rear and detectors 3 of the strip 2 and the rolling mill 1 and a heating control part 17 which clamps the specified length of the tip or the rear end of the strip 2 in the heating device 5 and moves the heating device 5 by the specified distance in synchronization with the strip passing speed while executing heating by the burner based on strip tip and rear end detection signals inputted from the tip and rear end detectors 3 of the strip 2 and the strip passing speed. Consequently, roll mark flaws of material to be rolled caused by the occurrence of the roll flaws can be obviated.