There is disclosed a fuel cell system or the like capable of sufficiently reducing an exhaust hydrogen concentration even in a case where a fuel cell is operated in a state of a low power generation efficiency. A bypass valve is arranged between an oxidation gas supply path and a cathode-off gas channel. In a state in which supply of an oxidation gas to a cathode falls short, pumping hydrogen is included in a cathode-off gas. Therefore, a valve open degree of the bypass valve is regulated, and a flow rate of bypass air is regulated to control the exhaust hydrogen concentration.