A control apparatus for a three-phase AC motor includes a current sensor and a current estimation section. The current sensor detects current flowing through one phase of the motor. The current estimation section repeats dq transformation and inverse dq transformation in a predetermined cycle. In the dq transformation, a d-axis current estimation value and a q-axis current estimation value in a rotating coordinate system of the AC motor are calculated based on the detected current and a previous current estimation value of another phase of the AC motor. In the inverse dq transformation, a present current estimation value of the other phase to be obtained at a time of angle advance of one period of the cycle is calculated based on smoothed values of the d-axis current estimation value and the q-axis current estimation value.