A connection structure includes a thin wall stainless steel pipe with a swelling portion, a sandwiching portion forming an inclined pressing surface capable of pressing an inclined surface of the swelling portion, a joint spacer forming a first retention portion pinching a first gasket with respect to the swelling portion as well as having a fitting portion fitted to an outer periphery of an end portion of the thin wall stainless steel pipe, and forming a gasket receiving portion in an outer peripheral side thereof, and a joint having a second retention portion sandwiching and pressing a second gasket to an inner peripheral side facing the gasket receiving portion.