A fuel cell system, comprising: a cathode gas supply passage configured to supply a fuel cell stack with a cathode gas; a cathode gas discharge passage configured to discharge the cathode gas supplied to the fuel cell stack; a compressor provided in the cathode gas supply passage; a bypass passage configured to discharge a part of the cathode gas discharged from the compressor to the cathode gas discharge passage while controlling the part of the cathode gas to bypass the fuel cell stack; a bypass valve that is provided in the bypass passage and that is configured to adjust a flow rate of the cathode gas flowing through the bypass passage in a stepwise manner; a stack supply flow rate detection unit configured to detect a flow rate of the cathode gas supplied to the fuel cell stack; a target stack supply flow rate setting unit configured to calculate a target supply flow rate of cathode gas to be supplied to the fuel cell stack based on a request from the fuel cell stack; a compressor-supply-flow-amount-requested-by-stack calculation unit configured to calculate a compressor supply flow rate requested by stack for controlling the stack supply flow rate to reach the target stack supply flow rate based on the stack supply flow rate and the target stack supply flow rate; a target compressor supply flow rate setting unit configured to set a larger one of the compressor supply flow rate requested by stack and a lower limit flow rate, which is determined depending on an operation state of the fuel cell system, as a target compressor supply flow rate, which is a target value of the compressor supply flow rate; a compressor control unit configured to control the compressor depending on the target compressor supply flow rate; a bypass valve control unit configured to control the bypass valve based on the stack supply flow rate and the target stack supply flow rate; a fixing unit configured to fix the bypass valve when the stack supply flow rate is in a predetermined bypass valve fixing range having the target stack supply flow rate as a reference, and the stack supply flow rate becomes less than the target stack supply flow rate; and a fixation releasing unit configured to release the fixation of the bypass valve when the target compressor supply flow rate becomes more than the lower limit flow rate after the fixing unit fixes the bypass valve. a cathode gas supply passage configured to supply a fuel cell stack with a cathode gas; a cathode gas discharge passage configured to discharge the cathode gas supplied to the fuel cell stack; a compressor provided in the cathode gas supply passage; a bypass passage configured to discharge a part of the cathode gas discharged from the compressor to the cathode gas discharge passage while controlling the part of the cathode gas to bypass the fuel cell stack; a bypass valve that is provided in the bypass passage and that is configured to adjust a flow rate of the cathode gas flowing through the bypass passage in a stepwise manner; a stack supply flow rate detection unit configured to detect a flow rate of the cathode gas supplied to the fuel cell stack; a target stack supply flow rate setting unit configured to calculate a target supply flow rate of cathode gas to be supplied to the fuel cell stack based on a request from the fuel cell stack; a compressor-supply-flow-amount-requested-by-stack calculation unit configured to calculate a compressor supply flow rate requested by stack for controlling the stack supply flow rate to reach the target stack supply flow rate based on the stack supply flow rate and the target stack supply flow rate; a target compressor supply flow rate setting unit configured to set a larger one of the compressor supply flow rate requested by stack and a lower limit flow rate, which is determined depending on an operation state of the fuel cell system, as a target compressor supply flow rate, which is a target value of the compressor supply flow rate; a compressor control unit configured to control the compressor depending on the target compressor supply flow rate; a bypass valve control unit configured to control the bypass valve based on the stack supply flow rate and the target stack supply flow rate; a fixing unit configured to fix the bypass valve when the stack supply flow rate is in a predetermined bypass valve fixing range having the target stack supply flow rate as a reference, and the stack supply flow rate becomes less than the target stack supply flow rate; and a fixation releasing unit configured to release the fixation of the bypass valve when the target compressor supply flow rate becomes more than the lower limit flow rate after the fixing unit fixes the bypass valve.