The invention relates to a shut down system and control method of the fuel cell vehicle. The shut down system of the fuel cell vehicle includes: a fuel cell configured to output a high voltage; a rechargeable high voltage battery; a bidirectional converter arranged between an output terminal of the fuel cell and the high voltage battery; a first relay arranged between the fuel cell and the bidirectional converter; and a controller configured to control a voltage of the bidirectional converter when the fuel cell vehicle stalls to reduce a voltage of the output terminal of the fuel cell and turnoff the first relay when a voltage value of the output terminal of the fuel cell is below a preset voltage reference value.