Method for producing pneumatic tire and pneumatic tire

A method for producing a pneumatic tire in which an air-in phenomenon between an inner liner and a carcass is avoided by preventing adhesion of the inner liner to a bladder includes the following steps. A green tire using, as an inner liner, a polymer laminate including a first layer (11a) having a thickness of 0.05 mm to 0.6 mm made of a styrene-isobutylene-styrene triblock copolymer, and a second layer (12a) composed of at least one of a second A layer made of a styrene-isoprene-styrene triblock copolymer and a second B layer made of a styrene-isobutylene diblock copolymer, the second layer having a thickness of 0.01 mm to 0.3 mm, is prepared. The green tire is mounted in a mold for vulcanization with pressurization by the bladder to obtain a vulcanized tire. The vulcanized tire is cooled at 50 to 120°C for 10 to 300 seconds.