Deterioration at the start-up and deterioration during the leaving period are suppressed in a good balance. As a system shutdown process, a controller (30) causes consumption of the air (oxygen) present in an oxidant electrode of a fuel cell stack (1) (oxygen consumption control). Further, after the termination of the oxygen consumption control, the controller (30) performs control to set a medium pressure hydrogen valve (13) and a hydrogen pressure adjustment valve (14) in a closed state. The controller (30) thereby causes hydrogen to be held in a passage located between the medium pressure hydrogen valve (13) and the hydrogen pressure adjustment valve (14). During a system shutdown period, a predetermined amount of hydrogen (medium pressure hydrogen) held in the hydrogen supply passage (L1) at a position between the medium pressure hydrogen valve (13) and the hydrogen pressure adjustment valve (14) can be supplied to the fuel electrode of the fuel cell stack (1) through a bypass passage (L2).