A fuel cell system, which can supply a stable flow rate of fuel to a fuel cell stack is disclosed. The fuel cell system may include a fuel cell stack for generating electricity by an electrochemical reaction of a fuel and an oxidizing agent, a fuel supply unit for supplying a fuel to the fuel cell stack, an oxidizing agent supply unit for supplying an oxidizing agent to the fuel cell stack, and a flow rate controller installed between the fuel cell stack and the fuel supply unit. The fuel cell system may include a feed pump for pressurizing the fuel, a first resistor connected to the front end of the feed pump to reduce flow rate and a second resistor connected to the rear end of the feed pump to reduce flow rate. A method of operating a fuel cell system is also disclosed. The method may include supplying fuel to a fuel cell stack from a fuel supply unit, reducing a flow rate by a first resistor, activating a feed pump, reducing a flow rate by a second resistor, and stopping the feed pump.