A tire member-forming apparatus comprising: a drum device comprising a wound body rotatably driven and having a non-straight cylindrical shape around which a rubber strip is wound; a rubber strip supply device to supply the rubber strip; a rubber strip sticking device comprising an applicator transporting the rubber strip supplied from the rubber strip supply device and winding the same around the wound body; the applicator comprising a transport conveyor comprising a transport belt for transporting the rubber strip on a transport surface, the transport belt being guided by a plurality of guide rollers in a manner capable of circling; the transport surface comprising a center line in a width direction extending linearly over the entire length of the transport surface; the guide rollers comprising front guide rollers comprising a foremost guide roller disposed on the foremost side of the transport direction and back guide rollers comprising a backmost guide roller disposed on the backmost side of the transport direction; and the front guide rollers being held in a manner capable of tilting around the center line of the transport surface in the width direction so that the transport surface forms a twistable transport surface portion between a front transport surface portion supported by the front guide rollers and a back transport surface portion supported by the back guide rollers, characterized in that the applicator comprises a press conveyor having a press belt guided by a plurality of upper guide rollers in a manner capable of circling, wherein the press belt presses the rubber strip against the transport belt, and the press belt comprises a press surface that is composed of a front press surface portion pressing the rubber strip against the front transport surface portion, a back press surface portion pressing the rubber strip against the back transport surface portion, and a twistable press surface portion pressing the rubber strip against the twistable transport surface portion. a drum device comprising a wound body rotatably driven and having a non-straight cylindrical shape around which a rubber strip is wound; a rubber strip supply device to supply the rubber strip; a rubber strip sticking device comprising an applicator transporting the rubber strip supplied from the rubber strip supply device and winding the same around the wound body; the applicator comprising a transport conveyor comprising a transport belt for transporting the rubber strip on a transport surface, the transport belt being guided by a plurality of guide rollers in a manner capable of circling; the transport surface comprising a center line in a width direction extending linearly over the entire length of the transport surface; the guide rollers comprising front guide rollers comprising a foremost guide roller disposed on the foremost side of the transport direction and back guide rollers comprising a backmost guide roller disposed on the backmost side of the transport direction; and the front guide rollers being held in a manner capable of tilting around the center line of the transport surface in the width direction so that the transport surface forms a twistable transport surface portion between a front transport surface portion supported by the front guide rollers and a back transport surface portion supported by the back guide rollers, the applicator comprises a press conveyor having a press belt guided by a plurality of upper guide rollers in a manner capable of circling, wherein the press belt presses the rubber strip against the transport belt, and the press belt comprises a press surface that is composed of a front press surface portion pressing the rubber strip against the front transport surface portion, a back press surface portion pressing the rubber strip against the back transport surface portion, and a twistable press surface portion pressing the rubber strip against the twistable transport surface portion.