To provide a connection structure capable of connecting a not-processed pipe, of which an end part is left as it is cut off without being flared, with an existing flared joint male member when replacing a flared joint which is connected by a flared joint.

In the connection structure for connecting the not-processed pipe 5 of which end part 4 is left as it is cut off without being flared with the metal male member 3 for the flared joint having a tip end contracting tapered part 1 and a male screw part 2, a metallic cylinder member 9 has a female screw part 7 for screwing with the male screw part 2 at an end 6 side and the not-processed pipe 5 is inserted from another end 8 side to the metallic cylinder member 9. The cylinder member 9 has a tapered inner circumferential surface 10 corresponding to the tip end contracting tapered part 1. A recessed circumferential groove part 12 is provided in an inner circumferential surface 11 of the cylinder member 9 and an elastic sealing member 13 is provided in the recessed circumferential groove part 12.