An apparatus and method for controlling an inverter capable of enhancing reliability of current measurement by ensuring an optimal time for which effective voltage vectors are applied to detect a three-phase current according to a phase current and sizes of the effective voltage vectors, the apparatus comprising a space voltage modulator that generates and outputs effective voltage vectors based upon a voltage command value, and a low modulation determiner that determines whether the effective voltage vectors are located within a low modulation region, and outputs a low modulation switching control signal or a normal modulation switching control signal according to the determination.