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 (Vcap_O) of the capacitor from a detected current (Icap) of the capacitor, an output voltage (Vout) of the fuel cell, and an internal resistance (Rcap) of the capacitor. A corrective quantity calculator calculates a corrective quantity (Ifc_AM) for a target supply current (Ifc_REQ) based on the open voltage (Vcap_O) of the capacitor, the output voltage (Vout) of the fuel cell, and the target supply current (Ifc_REQ), 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 (Icap−Vcap) of the fuel cell and current-voltage characteristic data (Ifc−Vcap) of the capacitor.