A fuel cell system comprising: a fuel cell; a combustor configured to combust a fuel and an oxidizing gas to supply a combustion gas to a cathode inlet of the fuel cell; a combustion fuel supply device configured to supply a fuel to the combustor; a combustion oxidizing gas supply device configured to supply an oxidizing gas to the combustor; an anode-discharged-gas discharge passage configured to discharge an anode discharged gas from an anode outlet of the fuel cell; a cathode-discharged-gas discharge passage configured to discharge a cathode discharged gas from a cathode outlet of the fuel cell; and a controller configured to control a supply of the fuel to the combustor by the combustion fuel supply device and a supply of the oxidizing gas to the combustor by the combustion oxidizing gas supply device, wherein the controller includes: a post-stop-request combustor-supply control unit configured to execute the supply of the fuel and the supply of the oxidizing gas to the combustor as an anode degradation reduction process after a request for stopping the fuel cell system, and an anode degradation reduction processing unit configured to perform another anode degradation reduction process in a case where the oxygen partial pressure of an anode pole of the fuel cell becomes equal to or more than a predetermined upper limit threshold value after the request for stopping the fuel cell and during supply of a fuel and an oxidizing gas, wherein the another anode degradation reduction process comprises at least one of: a reverse voltage application process configured to apply an electromotive force reverse to the fuel cell; and a fuel cell fuel supply process configured to supply a fuel to the fuel cell, and the predetermined upper limit threshold value is a value of the oxygen partial pressure where a degree of oxidative degradation of the anode pole possibly occurs. a fuel cell; a combustor configured to combust a fuel and an oxidizing gas to supply a combustion gas to a cathode inlet of the fuel cell; a combustion fuel supply device configured to supply a fuel to the combustor; a combustion oxidizing gas supply device configured to supply an oxidizing gas to the combustor; an anode-discharged-gas discharge passage configured to discharge an anode discharged gas from an anode outlet of the fuel cell; a cathode-discharged-gas discharge passage configured to discharge a cathode discharged gas from a cathode outlet of the fuel cell; and a controller configured to control a supply of the fuel to the combustor by the combustion fuel supply device and a supply of the oxidizing gas to the combustor by the combustion oxidizing gas supply device, wherein the controller includes: a post-stop-request combustor-supply control unit configured to execute the supply of the fuel and the supply of the oxidizing gas to the combustor as an anode degradation reduction process after a request for stopping the fuel cell system, and an anode degradation reduction processing unit configured to perform another anode degradation reduction process in a case where the oxygen partial pressure of an anode pole of the fuel cell becomes equal to or more than a predetermined upper limit threshold value after the request for stopping the fuel cell and during supply of a fuel and an oxidizing gas, wherein a post-stop-request combustor-supply control unit configured to execute the supply of the fuel and the supply of the oxidizing gas to the combustor as an anode degradation reduction process after a request for stopping the fuel cell system, and an anode degradation reduction processing unit configured to perform another anode degradation reduction process in a case where the oxygen partial pressure of an anode pole of the fuel cell becomes equal to or more than a predetermined upper limit threshold value after the request for stopping the fuel cell and during supply of a fuel and an oxidizing gas, wherein the another anode degradation reduction process comprises at least one of: a reverse voltage application process configured to apply an electromotive force reverse to the fuel cell; and a fuel cell fuel supply process configured to supply a fuel to the fuel cell, and a reverse voltage application process configured to apply an electromotive force reverse to the fuel cell; and a fuel cell fuel supply process configured to supply a fuel to the fuel cell, and the predetermined upper limit threshold value is a value of the oxygen partial pressure where a degree of oxidative degradation of the anode pole possibly occurs.