An anode non-circulation type fuel cell sets an anode upper limit pressure and an anode lower limit pressure, and sets an anode pressure increase rate based on at least a detected temperature of a fuel cell. The system controls the supply of an anode gas to the fuel cell so as to repeat pressure increase and pressure decrease. The pressure increase is conducted by supplying the anode gas to the anode upper limit pressure at the anode pressure increase rate. The pressure decrease is conducted by restricting the supply of the anode gas to the anode lower limit pressure. When the detected temperature of the fuel cell is lower than a predetermined temperature, the system sets the anode pressure increase rate at a slower rate than when the temperature of the fuel cell is equal to or higher than the predetermined temperature.