A pipe-connecting device in which the device includes: an inner ring having; an outer circumferential portion in which a tip-contracted outer-circumferential flared surface that is press-insertable from a tip end into an end portion of a fluid transfer tube made of a fluorine resin to flare an inner circumferential portion of the end portion of the tube is formed at the tip end; and an inner circumferential portion constituting a fluid transfer path; a pipe joint body or fluid apparatus that has a tubular screwing portion in which an external thread is formed on an outer circumferential side; and a union nut in which an internal thread that is screwed with the external thread of the tubular screwing portion is formed, the inner ring is insertable into the tubular screwing portion in a state where the inner circumferential portion of the end portion of the tube is flared, and the outer-circumferential flared surface is pressed against the union nut which is screwed with the external thread of the tubular screwing portion, in a state where the tube is clamped, wherein a pressing portion which is in the union nut, and is configured to press the tube against the outer-circumferential flared surface is formed into an inclined inner circumferential surface which is inclined in a same direction as the outer-circumferential flared surface with respect to an axis of the tubular screwing portion, characterized in that the outer-circumferential flared surface is formed into a convex curved surface with respect to the longitudinal axis, and in a cross section including the axis, the largest angle (θ) of inclination of a tangent line to a profile of the inner circumferential surface of the pressing portion with respect to the axis is larger than the largest angle (α) of inclination of a straight line with respect to the axis, and the straight line connects a first point (a) and a second point (c), at which the outer-circumferential flared surface has the maximum and minimum diameters, respectively. an inner ring having; an outer circumferential portion in which a tip-contracted outer-circumferential flared surface that is press-insertable from a tip end into an end portion of a fluid transfer tube made of a fluorine resin to flare an inner circumferential portion of the end portion of the tube is formed at the tip end; and an inner circumferential portion constituting a fluid transfer path; a pipe joint body or fluid apparatus that has a tubular screwing portion in which an external thread is formed on an outer circumferential side; and a union nut in which an internal thread that is screwed with the external thread of the tubular screwing portion is formed, the inner ring is insertable into the tubular screwing portion in a state where the inner circumferential portion of the end portion of the tube is flared, and the outer-circumferential flared surface is pressed against the union nut which is screwed with the external thread of the tubular screwing portion, in a state where the tube is clamped, wherein a pressing portion which is in the union nut, and is configured to press the tube against the outer-circumferential flared surface is formed into an inclined inner circumferential surface which is inclined in a same direction as the outer-circumferential flared surface with respect to an axis of the tubular screwing portion, characterized in that the outer-circumferential flared surface is formed into a convex curved surface with respect to the longitudinal axis, and in a cross section including the axis, the largest angle (θ) of inclination of a tangent line to a profile of the inner circumferential surface of the pressing portion with respect to the axis is larger than the largest angle (α) of inclination of a straight line with respect to the axis, and the straight line connects a first point (a) and a second point (c), at which the outer-circumferential flared surface has the maximum and minimum diameters, respectively.