A molded article of a thermoplastic resin with good apperance which may have a skin material is produced by providing upper and lower molds having a product part-molding section and a non-product part-molding section, supplying a melt of a thermoplastic resin in a cavity of the molds or a space between the skin material and either one of the upper and lower molds through a resin melt passage which is formed in a wall of one of the molds and has an opening for supplying the melt in the non-product part-molding section when a clearance of the cavity is larger than a thickness of a finally produced article, closing the molds to effect press molding, cooling the molds.