PURPOSE: To eliminate the loose winding of a first winding, tightly wind a strip on a mandrel from the first winding, thus, early release a wrapper roll and enhance the tracing accuracy of the tip of the strip.

CONSTITUTION: This device is equipped with a tip detector 24 detecting the tip of a strip 1, which is installed on the upstream side from a mandrel 6, and a tracking device 26 tracking the position of the tip of the strip by receiving the signal of the tip detector. Timing at which the tip of the strip is passed through each wrapper roll 7, is detected by a roll controller 22. Just after the tip of the strip of the first winding passed through each wrapper roll, the control of the wrapper roll is changed over from a position control to a pressing force control, and each wrapper roll is pressed against the mandrel. Consequently, the strip is wound on the mandrel.