A control apparatus for a fuel cell stack includes a fuel cell stack having a stacked body formed by stacking fuel cell units together and a pair of end plates sandwiching the stacked body therebetween; electrical heaters disposed near the ends of the stacked body or the end plates, respectively; a water purging device for purging water which is generated during a power generation operation in the fuel cell stack, and which is held in the fuel cell units; and a control unit which controls the power generation operation in the fuel cell stack, and which is operatively connected to the electrical heaters and the water purging device. The control unit is adapted to operate the electrical heaters and the water purging device when the power generation operation is stopped.