Disclosed are a fuel cell system, and a method of driving the system. The fuel cell system includes a fuel cell stack having a plurality of unit cells producing electricity, a switching unit connecting the plurality of unit cells to a discharge resistor, a switching controller synchronously operated when the voltage of the fuel cell stack reaches an open circuit voltage after power generation of the fuel cell stack is stopped. The switching controller generates select control signals to control the switching unit. The fuel cell system further includes a sensing unit measuring respective cell voltages of the plurality of unit cells and generating cell voltage sensing signals to control activation periods of the select control signals.