A control device for an AC rotary machine includes an AC rotary machine having x-phase windings where x is at least three, an angle detector, a current detector, a voltage command calculator, and a power converter, wherein, when a current of at least one phase of the x phases is detectable and currents of at most (x−1) phases are undetectable at a present current detection timing, the current detector estimates the currents of the (x−1) phases that are undetectable at the present current detection timing by calculation on the basis of detected currents of x phases obtained at a past current detection timing, the detected current of the single phase that is detectable at the present current detection timing, and an angle variation amount from the past current detection timing to the present current detection timing.