A connecting method and structure is provided to reliably ensure the compressive strength of the joint between a heat transfer pipe and a capillary tube when connecting the capillary tube to the heat transfer pipe by direct brazing. In the connection structure between the heat transfer pipe and the capillary tube, a pinched part in which a pipe end part of the capillary tube is inserted and a brazing filler material pooling part for pooling on a pipe end face side of the pinched part the brazing filler material that flows into the pinched part are formed. When inserted into the pinched part, the capillary tube is brazed to the heat transfer pipe.