An apparatus and method for controlling cooling of electronic components of a fuel cell vehicle are provided. The apparatus for controlling cooling of electronic components connected in series and parallel with a coolant loop in a fuel cell vehicle using a pump includes a monitor configured to collect measured temperature of the electronic components and a measured temperature of a coolant through a plurality of temperature sensors, and a controller configured to control the RPM of the pump based on the measured temperatures and at least one of electronic component temperature maps, a coolant temperature map and a temperature difference map representing temperature differences between the electronic components and coolant, the controller controlling the RPM of the pump using over-temperature set information and over-temperature reset information of each temperature map.