A fuel cell vehicle may include: an electric traction motor; an inverter; a fuel cell system; a first boost converter including first low voltage terminals connected to a fuel cell and first high voltage terminals connected to the inverter, the first boost converter including a first capacitor connected between positive and negative terminals of the first high voltage terminals; a first relay connected between the first boost converter and the inverter; and a controller, wherein the controller is configured to: shut down the fuel cell system; while a voltage of the fuel cell is higher than a voltage threshold, discharge the first capacitor and maintain a voltage thereof higher than the voltage of the fuel cell; and when the voltage of the fuel cell becomes lower than the voltage threshold, stop discharging the first capacitor and disconnect the first boost converter from the inverter by opening the first relay.