The invention can surely accomplish lamination without the generation of voids in building a tire constructed to comprise a plurality of rubber members for a tire when a ribbon-shaped rubber strip (R) is spirally wound and laminated, and uses holding rolls (30) and two sets of stitching rolls (40a), (40b) arranged in parallel with a center of a rubber strip width (W) therebetween to enable performing of an independent pressing motion, such that the rubber strip (R) is pressed and bonded by the holding rolls (30) in a position, in which the rubber strip (R) is wound, and the stitching roll (40a) or (40b) positioned fore in an advancing direction of traverse movement, out of the two sets, is caused to perform a pressing motion in a regional part just after the press whereby a fore part of the rubber strip in the advancing direction is pressed and bonded.