To surely prevent dropping-out of an outer pipe from a joint regardless of the wall thickness of the outer pipe in connection of a double pipe to the joint.

In the structure for connecting, to the joint 1, the double pipe having the outer pipe 21 formed of a synthetic resin heat-insulating foam and a flexible inner pipe 11 inserted inside the outer pipe 21, an end portion of the inner pipe 11 is connected to an inside cylindrical portion 5 formed on the joint 1, an end portion of the outer pipe 21 is fitted onto an outside cylindrical portion 6 formed outside the inside cylindrical portion 5, and a pair of locking projections 34, 34 of a stopping member 31 is inserted to the internal space of the outer pipe 21 from the outer periphery side with the outer pipe 21 being fitted onto the outside cylindrical portion 6, and directly locked on a locked portion 7a formed in a recessed portion of a confirmation window 7 of the outside cylindrical portion 6, whereby the outer pipe 21 is prevented from being dropped out of the joint 1.