A high-pressure fuel injection pipe having connecting head portion is provided which is capable of eliminating a fear of the occurrence of cavitation erosion of the inner surface of the connecting head portion and a fatigue failure of the same head portion by having a contour of a cross section of an annular pocket occurring in an inner part of the connecting head portion during a head portion processing operation extend shallowly and gently. This fuel injection pipe has at a connecting end portion of a thick-walled steel pipe having a relatively small diameter, including a seat surface, an annular flange formed so that the flange is axially spaced from the seat surface, and a conical surface connected to the seat surface, extending therefrom to the annular flange and tapering off to a free end of the connecting head portion, wherein the conical surface is provided at a part thereof with an annular, shallow, cross-sectionally curved recess.