To provide an air supply/discharge structure capable of surely controlling and preventing generation of a short cycle even it has tendency to lower a flow rate of an exhaust gas in comparison with a conventional one.

A flange member 5, an exhaust top 4 and an exhaust cover 6 are connected with a tip of an exhaust cylinder 3 inserted into a mounting hole 21 of an external wall 2 of a building, and fixed to the external wall by the flange member. A through hole 61 of an opening area smaller than a passage cross-section of the exhaust cylinder, is formed on the exhaust cover to increase a speed of the exhaust gas passing therethrough. A drain receiver is defined on an inner bottom portion of the exhaust cover, and a recessed groove portion 65 is formed on a lowermost portion of the through hole. Exhaust gas drain is discharged to the drain receiver from the exhaust cylinder and the exhaust top, and and allowed to overflow from the recessed groove portion when it increases.