At the time of transfer of a strip-shaped rubber member (15) onto a belt conveyor (12) by a transfer unit, support members (61), each of which is provided on one width-direction side of a corresponding belt (51) and is projectable from a conveying surface of the belt (51), are lifted by a lifting/lowering unit (71) to project from the conveying surface of the belts (51), so that the strip-shaped rubber member (15) is raised from the conveying surface of the belts (51). Therefore, the strip-shaped rubber member (15) is not in sliding contact with the conveying surface of the belts (51) at the time of transfer. As a result, a situation whereby the belts (51) are dragged by the strip-shaped rubber member (15) so that one width-direction edge portion thereof is turned up can be prevented.