A method and apparatus for controlling output of a fuel cell are provided. The apparatus includes a communicator that is configured to receive state information of a fuel cell and a controller that is configured to terminate charge of a battery by a power converting apparatus when a first voltage of the fuel cell is less than a preset second voltage as air supply of the fuel cell is stopped. Additionally, the controller is configured to activate a relay between the fuel cell and the battery to charge the battery when the first voltage is less than the second voltage.