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 insertable from a tip end into a tube end portion of a fluid transfer tube made of a resin to flare the tube end portion is formed at a 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 circumference; and a union nut in which an internal thread that is to be screwed with the external thread is formed, the inner ring being insertable into the tubular screwing portion in a state where the tube end portion is flared, and the tip-contracted outer-circumferential flared surface is pressable against the union nut which is screwable with the external thread, with the tube clamped, the pipe-connecting device being connectable to the tube, characterized in that a tube pressing portion which is in the union nut, configured to press the tube against the tip-contracted outer-circumferential flared surface is formed into an inclined inner circumferential surface which is inclined in a same direction as the tip-contracted outer-circumferential flared surface with respect to an axis of the tubular screwing portion, and the tip-contracted outer-circumferential flared surface forms a convex curved surface in which the whole is convex radially and outwardly in an axis direction of the inner ring, as a press-contact portion configured to make the tip-contracted outer-circumferential flared surface be in contact with the inner circumferential portion of the tube end portion, prior to fastening of the union nut, between the tip-contracted outer-circumferential flared surface and the inner circumferential portion of the tube end portion, wherein an angle (θ) of the inclined inner circumferential surface with respect to the axis is set to be larger than an angle (α) formed by a straight line connecting a place (a) where the pressing fitting portion, in which the tip-contracted outer-circumferential flared surface is configured to be in close contact with the tube end portion, has the maximum diameter and a place (c) where the tip-contracted outer-circumferential flared surface has the minimum diameter, and the axis. an inner ring having: an outer circumferential portion in which a tip-contracted outer-circumferential flared surface that is insertable from a tip end into a tube end portion of a fluid transfer tube made of a resin to flare the tube end portion is formed at a 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 circumference; and a union nut in which an internal thread that is to be screwed with the external thread is formed, the inner ring being insertable into the tubular screwing portion in a state where the tube end portion is flared, and the tip-contracted outer-circumferential flared surface is pressable against the union nut which is screwable with the external thread, with the tube clamped, the pipe-connecting device being connectable to the tube, characterized in that a tube pressing portion which is in the union nut, configured to press the tube against the tip-contracted outer-circumferential flared surface is formed into an inclined inner circumferential surface which is inclined in a same direction as the tip-contracted outer-circumferential flared surface with respect to an axis of the tubular screwing portion, and the tip-contracted outer-circumferential flared surface forms a convex curved surface in which the whole is convex radially and outwardly in an axis direction of the inner ring, as a press-contact portion configured to make the tip-contracted outer-circumferential flared surface be in contact with the inner circumferential portion of the tube end portion, prior to fastening of the union nut, between the tip-contracted outer-circumferential flared surface and the inner circumferential portion of the tube end portion, wherein an angle (θ) of the inclined inner circumferential surface with respect to the axis is set to be larger than an angle (α) formed by a straight line connecting a place (a) where the pressing fitting portion, in which the tip-contracted outer-circumferential flared surface is configured to be in close contact with the tube end portion, has the maximum diameter and a place (c) where the tip-contracted outer-circumferential flared surface has the minimum diameter, and the axis.