A production method including: a step of forming, on a substrate layer containing a polypropylene resin or a polyester resin, a metal oxide layer by a vacuum film forming process; a step of applying a gas barrier coating layer-forming composition on the metal oxide layer to form a coating film; a step of preheating the coating film by infrared radiation; and a step of heating and thereby curing the coating film preheated by infrared radiation in an atmosphere at 50 to 120° C. to form a gas barrier coating layer, in which the gas barrier coating layer-forming composition contains at least one selected from the group consisting of an alkyl silicon alkoxide and its hydrolysate, and a water-soluble polymer.