A system and method are arranged to control a low voltage DC converter of a fuel cell vehicle, in which, although a CAN communication timeout where the low voltage DC converter does not receive an off command from a vehicle control unit or a CAN communication failure occurs, when an output current of the low voltage DC converter is lowered by at least a predetermined value, the low voltage DC converter is turned off by itself by determining that a post-treatment operation of a fuel cell system is completed, and after the low voltage DC converter is turned off, a relay of a high voltage battery is opened, thereby preventing the relay of the high voltage battery from fusing.