Abstract: A molding system for molding a plastic grip member and, at the same time, linking it to a linking protruding piece of a container closure body. The molding system comprises a rotary container closure body conveyor apparatus and a compression molding apparatus. The container closure body conveyor apparatus is provided with a rotary disc that has a plurality of container closure body-receiving portions formed therein and a rotation preventing mechanism that prevents the rotation of the container closure bodies held in the receiving portions. The compression molding apparatus has a mold constituted by a first mold portion and a second mold portion. The first mold portion includes a moving member that moves between a mold position and a separated position. The moving member has a supporting surface for supporting the skirt wall of the container closure body and a support projection for supporting the linking protruding piece of the container closure body.