A pilferproof plastic closure comprising a top panel wall and a cylindrical skirt wall extending downwardly from the peripheral edge of the top panel wall. A circumferential weakening line extending circumferentially is formed in the skirt wall, and the skirt wall is divided into a main portion above the weakening line and a pilferproof bottom portion beneath it. An internal thread to be screwably fitted with an external thread formed on the mouth-neck portion of a container is formed on the inner surface of the main portion, and a plurality of radially inwardly projecting and circumferentially spaced engaging flaps are formed on the inner surface of the pilferproof bottom portion. An axial breaking line is formed in the pilferproof bottom portion which extends downwardly from the upper end of the pilferproof bottom portion but is non-existent in at least a greater portion of the lower part of the pilferproof bottom portion. At least a greater portion of the base edge of each of the engaging flaps is positioned in the aforesaid lower part where the axial breaking line does not exist.