A fuel cell system and a method for driving a fuel cell system are disclosed. The fuel cell system includes a fuel cell stack with a plurality of unit cells, a temperature measurer configured for determining a temperature of the fuel cell stack, a cell voltage measurer configured for determining voltages of one or more of the plurality of unit cells, and a control unit configured for monitoring the unit cell voltages of the plurality of unit cells to detect a minimum unit cell voltage when a measured temperature of the fuel cell stack is below zero, and configured for controlling the load current so that the detected minimum unit cell voltage may be maintained at a predetermined threshold voltage.