A fuel cell system, comprising: a cathode gas supply passage through which cathode gas is supplied to a fuel cell stack; a compressor provided on the cathode gas supply passage; a bypass passage through which a part of the cathode gas discharged from the compressor is eliminated by bypassing the fuel cell stack; a bypass valve provided on the bypass passage, the bypass valve being configured to adjust a flow rate of the cathode gas flowing through the bypass passage; a flow rate sensor configured to detect a stack supply flow rate supplied to the fuel cell stack; and a control unit programmed to perform: calculating a stack request compressor supply flow rate according to at least one of a compressor supply flow rate for generating electrical power required to the fuel cell stack, a compressor supply flow rate for controlling a degree of wetness of the fuel cell stack, and a compressor supply flow rate for preventing flooding in the fuel cell stack; calculating a system request compressor supply flow rate according to at least one of a compressor supply flow rate for setting a hydrogen concentration in the exhaust gas from the fuel cell system to a predetermined value or less, and a compressor supply flow rate for preventing surging in the compressor; setting larger one of the calculated stack request compressor supply flow rate and the calculated system request compressor supply flow rate as a target compressor supply flow rate; controlling the compressor based on the set target compressor supply flow rate; controlling the bypass valve based on the stack supply flow rate detected by the flow rate sensor and a target stack supply flow rate to be supplied to the fuel cell stack; and fixing the bypass valve or limiting driving of the bypass valve when the system request compressor supply flow rate is set as the target compressor supply flow rate and the stack supply flow rate becomes smaller than the target stack supply flow rate. a cathode gas supply passage through which cathode gas is supplied to a fuel cell stack; a compressor provided on the cathode gas supply passage; a bypass passage through which a part of the cathode gas discharged from the compressor is eliminated by bypassing the fuel cell stack; a bypass valve provided on the bypass passage, the bypass valve being configured to adjust a flow rate of the cathode gas flowing through the bypass passage; a flow rate sensor configured to detect a stack supply flow rate supplied to the fuel cell stack; and a control unit programmed to perform: calculating a stack request compressor supply flow rate according to at least one of a compressor supply flow rate for generating electrical power required to the fuel cell stack, a compressor supply flow rate for controlling a degree of wetness of the fuel cell stack, and a compressor supply flow rate for preventing flooding in the fuel cell stack; calculating a system request compressor supply flow rate according to at least one of a compressor supply flow rate for setting a hydrogen concentration in the exhaust gas from the fuel cell system to a predetermined value or less, and a compressor supply flow rate for preventing surging in the compressor; setting larger one of the calculated stack request compressor supply flow rate and the calculated system request compressor supply flow rate as a target compressor supply flow rate; controlling the compressor based on the set target compressor supply flow rate; controlling the bypass valve based on the stack supply flow rate detected by the flow rate sensor and a target stack supply flow rate to be supplied to the fuel cell stack; and fixing the bypass valve or limiting driving of the bypass valve when the system request compressor supply flow rate is set as the target compressor supply flow rate and the stack supply flow rate becomes smaller than the target stack supply flow rate. calculating a stack request compressor supply flow rate according to at least one of a compressor supply flow rate for generating electrical power required to the fuel cell stack, a compressor supply flow rate for controlling a degree of wetness of the fuel cell stack, and a compressor supply flow rate for preventing flooding in the fuel cell stack; calculating a system request compressor supply flow rate according to at least one of a compressor supply flow rate for setting a hydrogen concentration in the exhaust gas from the fuel cell system to a predetermined value or less, and a compressor supply flow rate for preventing surging in the compressor; setting larger one of the calculated stack request compressor supply flow rate and the calculated system request compressor supply flow rate as a target compressor supply flow rate; controlling the compressor based on the set target compressor supply flow rate; controlling the bypass valve based on the stack supply flow rate detected by the flow rate sensor and a target stack supply flow rate to be supplied to the fuel cell stack; and fixing the bypass valve or limiting driving of the bypass valve when the system request compressor supply flow rate is set as the target compressor supply flow rate and the stack supply flow rate becomes smaller than the target stack supply flow rate.