A system and method that compares an input voltage value through the input terminal of the LDC with a setting voltage in an ignition on-state and an on-state of a main relay for connection of a high-voltage battery Then a verification is made whether the main relay is in the on-state and whether the voltage of an input capacitor in an inverter is in a normal voltage range. As a result a diagnosis is made whether the disconnection of the input fuse has occurred in a low-voltage state when the input voltage is no more than the setting voltage and the on-state of the main relay and the state in which the voltage of the input capacitor in the inverter is in the normal voltage range.