The present invention provides a method of producing a tire component member, which method allows rubber strip pieces to be sequentially attached without forming a gap therebetween. A method of producing a tire component member by diagonally and sequentially attaching a rubber strip piece 1 having an elongated parallelogram-like shape in the circumferential direction on an outer peripheral curved face of a drum 5 having a curved face including the center portion more expanded than respective side portions, comprising the steps of: sequentially holding by adhesive force the rubber strip piece 1 from a leading end thereof, with a disposition of the rubber strip piece inclined by a predetermined angle with respect to the drum 5 having a curved face, by an adhesive drum 11 capable of holding by adhesive force the rubber strip 1 piece onto a peripheral surface thereof, while the adhesive drum is rotated; and press-attaching the rubber strip piece 1 held by adhesive force continuously from the leading end thereof, onto an outer peripheral curved face of the drum 5 having a curved face which is being rotated, while the rubber strip piece is moved along the direction of the rotation axis of the drum 5 having a curved face within a predetermined range, to transfer the rubber strip piece to the drum having a curved face.