PURPOSE: To effectively prevent the zig-zagged deformation of a tire constituent material by a method in which plural press rollers are wholly pressed only at the beginning of bonding the tire constituent material, and by using a part of the press rollers, only the longer peripheral portion is pressed.

CONSTITUTION: The tip of a material W1 is sent out onto a tire constituent material W already bonded to the upside of a tire molding drum 100. Under the condition, only an adequate section is only pressed by both press rolls 21 and 42, and then a cylinder 30 is operated to turn a shaft 10, whereupon the press roll 42 is opened since the shaft 40 is separated from the direction of the drum by off-center amount β set in the plate 12. The press roll 21 is continuously pressed by the cylinder 5. Afterwards, when the pressing process is completed, the arm 3 is pulled up by the cylinder 5, the roll 21 is opened, and the pressing operation is completed.