An apparatus for controlling an inverter for a motor driving includes: a current controller configured to generate a d/q-axis voltage reference for allowing a d/q-axis current detection value, which is obtained by measuring a current supplied from the inverter to the motor, to converge on the d/q-axis current reference for driving the motor, and a voltage modulator configured to control switching of the inverter by selectively applying one among a plurality of predetermined pulse width modulations (PWM) based on a point at which the d/q-axis voltage reference is located in a hexagonal space voltage vector diagram.