Abstract: In the manufacture of an inflation film for forming a thermoplastic resin having a melt tension of not more than 4 g into a tubular bubble, a tubular bubble extruded from an extruding nozzle is cooled from the inner circumferential surface thereof by air supplied from a first air supply opening. The outer circumferential surface of the bubble is cooled with air from a first external air-cooling ring arranged at the outside of the bubble. The first air-cooling ring has a guide plate for guiding the bubble, a second air supply opening for supplying air between the guide plate and the bubble from an inlet port arranged at the lower end of the guide plate, and a third air supply opening for supplying air to the bubble from an outlet port arranged at the upper end of the guide plate. The bubble which is cooled by the first external air-cooling ring is further cooled by the air supplied from a second external air-cooling ring. The bubble is solidified.