The present invention provides a cooling apparatus of a fuel cell vehicle in which a cooling efficiency of a fuel cell cooling heat exchanger located downstream of an air conditioner external heat exchanger does not decrease. (1) In the cooling apparatus, the air conditioner external heat exchanger and the fuel cell cooling heat exchanger are partially offset from each other so that a high-temperature portion of the air conditioner external heat exchanger is not overlapped with the fuel cell cooling heat exchanger in a front view taken from a front side of the vehicle. (2) A portion of the fuel cell cooling heat exchanger extending beyond an end of the air conditioner exterior heat exchanger opposite the high-temperature portion is disposed outside a fan shroud so as to be cooled by a vehicle-running wind only.