A fuel cell system including a fuel cell stack having a plurality of unit cells is provided. A method of driving the fuel cell stack is also provided. The method may include supplying a fuel to a fuel cell stack, supplying an oxidizer to the fuel cell stack, controlling supply of the fuel and the oxidizer to operate the fuel cell stack, calculating a total operation time of the fuel cell, and/or varying a stack activation period in which the oxidizer is blocked to the fuel cell stack according to the total operation time and a stack activation cycle of which the stack activation period is generated.