A transparent thin bottle-shaped container is produced by means of a technology for biaxial orientation blow molding a cylindrical piece with a bottom from polyethylene terephthalate material. The pieces are molded in large number in each injection molding process of an injection molding machine. The pieces thus formed immediately after the injection molding are held simultaneously in large number at the gates integrally projected therefrom by a base plate moved forward at the front of the mold in the injection molding machine. They are then conveyed to a gate cutting unit provided near the injection molding machine. The gates are cut from the pieces sequentially by the gate cutting unit and are conveyed onto a conveyor. The pieces are gradually cooled from the hot molded temperature during the conveyance and are additionally cooled while being conveyed on an oblique conveyor installed with a cooler to room temperature or lower predetermined temperature. The cooled pieces are then supplied to a heater immediately before entering a biaxial orientation blow molding process.