An apparatus for winding a belt-like member and a method of feeding a belt-like member for helically winding a belt-like member of a small width around an outer periphery of a rotating body which is rotatable about an axis of rotation and whose radius from the axis of rotation to the outer periphery thereof changes in correspondence with an axial position. A holding device is capable of holding a starting end of the belt-like member from both obverse and reverse surface sides thereof and of pressure-fitting the starting end of the belt-like member onto the rotating body. A feeding device moves the starting end of the belt-like member from a holding position where the belt-like member is held to the rotating body by moving the holding device, so as to feed the belt-like member to the rotating body.