An apparatus and a method for feeding an elongated strip onto a tire component building drum are especially adapted for applying breaker strips to giant radial tire breaker building drums. The apparatus includes a carriage with roller means for conveying the strip that is mounted on the same side of the building drum as the operator stands while applying the strip to the drum. The carriage is movable on a track on a frame mounted on a floor on which the operator stands, and the track and frame extend upwardly from the floor and are preferably slanted toward the drum. A roll of strip to be applied to the drum is contained in a roll support means near where the frame is mounted on the floor, and the strip is unwound from the roll and passed over rollers on the carriage and onto the drum. By moving the carriage on the track, the position of the carriage can be adjusted to the position that is best, in the judgment of the operator, for applying the strip to the drum.