A container closure for an additive includes: a storage member having an outlet port formed in the lower side surface of a tubular inner cap arranged inside the entrance of the container in a main cap coupled to the entrance of the container; an opening member which has a slider sliding in the vertical direction in the inner cap, and is coupled to an extended tube extending upwardly from the main cap; a bottom gasket which closes the lower end and inner surface of the slider, is hooked onto the storage member, and is separated from the slider when separating the opening member; and a bottom inner cap which is integrally formed with the lower end of the outlet port, and concurrently tightly seals the outer surface, the bottom surface, and the inner surface of the bottom gasket.