A control apparatus for an AC motor includes a current sensor and an estimation section. The current sensor detects current flowing through one phase of the motor. The estimation section repeats an estimation process. In the estimation process, d-axis and q-axis current estimation values are calculated based on the presently detected current of the one phase and a previous current estimation value of another phase of the motor, and a present current estimation value of each phase is calculated based on smoothed values of the d-axis and q-axis current estimation values. The estimation section performs the estimation process based on a phase lag element. The phase lag element is a difference between the presently detected current and a previous current estimation value of the one phase or the previously detected current.