When a preform having been molded while released from a mold at an earlier timing in an injection stretch blow molding machine is stretched and blow molded, the bottom of the preform is prevented from rupturing and the bottom of a hollow molded article is prevented from being uneven in wall thickness to produce such a hollow molded article without defect bottom by the injection stretch blow molding machine. An injection molding process of injection molding a preform; and a blow molding process of blow molding the preform to obtain a hollow molded article. The blow molding process allows a tip of a stretching rod cooled to a temperature between 50° C. and 90° C. to be brought into contact with the bottom of the preform in a softened state, and to press down the bottom of the preform while the bottom is cooled.