Control device of AC motor

A control device of a three-phase AC motor includes: an inverter that drives the AC motor; a current sensor that senses a current flowing in a sensor phase of the AC motor as a sensor phase current; and a controller that switches on and off a switching element of the inverter to control a current flowing through the AC motor. The controller includes: a current estimation device that estimates d-axis and q-axis current estimated values based on the sensor phase current and an electric angle of the AC motor; and a zero-crossing interpolation device that interpolates a command value relating to a voltage of the AC motor when the sensor phase current is in a zero cross range, which includes a zero point. When the sensor phase current is in the zero cross range, the zero-crossing interpolation device interpolates the command value with a continuous variable value.