A controller for an AC rotary machine, by which a stable rotation angular-frequency estimate (AFE) value can be obtained even in an extremely low speed region of the AC rotary machine is disclosed, and consequently stable control can be performed. The controller includes an AFE outputter that outputs an AFE value based on an angular-frequency calculated value including a rotation AFE value. The AFE outputter includes a lower-limit constant-value (LLCV) outputter that outputs a LLCV, a comparator that compares the angular-frequency calculated value to the LLCV, and a switcher that performs a switching operation according to the comparator. The switcher outputs the angular-frequency calculation value as the AFE value when the angular-frequency calculation value is larger than the LLCV, and outputs the LLCV as the AFE value when the angular-frequency calculation value is equal to or less than the LLCV.