A method of operating a fuel cell power generator, and a fuel cell power generator to be operated by the method, which method enables feeding of a diluted fuel having an optimum concentration to a power generation unit even without measuring an absolute concentration typically using a sensor are provided. Specifically, how an output voltage of the power generation unit varies depending on a flow rate of a diluted fuel is monitored. Thus, the diluted fuel may be adjusted to have an optimum concentration always, even without measuring an absolute concentration typically using a sensor. According to this operation method, output characteristics and electrical efficiencies can be maximized according to a load and conditions of a fuel cell power generator.