Provided is a fuel-cell system and a method of operating the fuel-cell system, wherein functions F=f(P) and P=f−1(F) of electrical output P and fuel flow-rate F required to output P are beforehand obtained, and a reformable fuel flow-rate FR is calculated from the temperature of reforming catalyst layer. When FR≧Fmin, if the output demand PD≦maximum output PM, and when f(PD)≦FR, F is set to f(PD); and when f(PD)>FR, the P is set to the maximum value within a range of less than PD amongst P calculated from P=f1(FR), and F is set to FR. When PD>PM, and when f(PM)≦FR, the cell output is set to PM, and F is set to f(PM). When f(PM)>FR, the cell output is set to the maximum value amongst P calculated from P=f1(FR), and F is set to FR.