To provide a connection structure of a joint which prevents leakage, does not easily slip out, and facilitates the adjustment of the length of a connection portion of the joint such as an elbow.

In the connection structure between a drain pipe and the joint, the end of the joint 2 is insertable into an outlet of the drain pipe 1. The outlet of the drain pipe 1 has a male screw 11 formed on the peripheral surface thereof which is screwed into a female screw 41 internally formed in a box nut 4 loosely fitted to the joint 2 via a triangular packing 3 beforehand. Further the joint 2 has a male screw 22 formed on the outer peripheral surface of the insertion end 21 thereof, and a female screw 12 screwable with the male screw 22 is internally formed in the deep-side inner peripheral surface of the outlet of the drain pipe 1.