In a controller for an AC rotating electric machine, a failure-state determining circuitry determines a failure state of a magnetic-pole position sensor based on an output signal from the magnetic-pole position sensor. A modulation-ratio switching circuitry outputs a target value of a modulation ratio and also changes the target value to be output based on a result of the failure-state determining circuitry. The modulation-ratio switching circuitry sets, when the magnetic-pole position sensor is determined as being abnormal by the failure-state determining circuitry, the target value to be smaller than in a case in which the magnetic-pole sensor is determined as being normal by the failure-state determining circuitry.