Abstract: A high pressure fuel injection pipe is produced by squeezing an end portion of a small-diametered steel pipe member having a flow path extending through the center thereof to form a flow path of reduced diameter in the end portion communicating with the central flow path, pressing and plastically shaping the end portion into a frusto-conical or arcuate-surfaced connecting head, and grinding minute curve concavo-convex faces created in the inner surface of the flow path of reduced diameter during the plastic shaping to thereby form a flow path equal in diameter and communicating with the flow path in the small-diametered steel pipe member.