The invention can perform building in a process for building a carcass band or a belt/tread band of a tire, in which two drum transfer support bases (10) supporting building drums (D1) are alternately shifted to first and second transfer sections (11), (12), in which predetermined building positions are set, a rotational transfer device (A) for rotational transfer of the drum transfer support bases (10) is mounted between the first transfer section (11) and the second transfer section (12), which are arranged to get out of position relative to and in parallel to each other, and two pairs of rotational transfer rails (27a), (28a) are juxtaposed on a rotating table (20), which has an axis (O) intermediate between the both transfer sections, to be positioned corresponding to extensions of travel rails (11a), (12a) arranged on the first and second transfer sections (11), (12) to receive two drum transfer support bases (10), (10), which enter from portions of the rails (11a), (12a) of the both transfer sections (11), (12), to have the same rotationally transferring to the other transfer section (12) or (11) at the same time.