A fuel cell power supply has a fuel cell and a capacitor which are connected parallel to each other, and controls the amount of a reacting gas supplied to the fuel gas based on a target supply current. A capacitor open voltage calculator calculates an open voltage of the capacitor from a detected current of the capacitor, an output voltage of the fuel cell, and an internal resistance of the capacitor. A corrective quantity calculator calculates a corrective quantity for a target supply current based on the open voltage of the capacitor, the output voltage of the fuel cell, and the target supply current, so as to prevent an air compressor from operating excessively and also prevent the fuel cell from suffering a gas shortage, depending on current-voltage characteristic data of the fuel cell and current-voltage characteristic data of the capacitor.