To provide a controller for AC rotary electric machine which can control considering the interlinkage fluxes of first-axis and second-axis which change mutually according to the currents of first-axis and second-axis, such as d-axis and q-axis. A controller for AC rotary electric machine calculates interlinkage flux model response values of first-axis and second-axis by performing a response delay processing of a model response to the interlinkage flux command values of first-axis and second-axis; and calculates voltage command values of first-axis and second-axis which make interlinkage fluxes of first-axis and second-axis change to the interlinkage flux model response values of first-axis and second-axis in a feedforward manner, based on the interlinkage flux model response values of first-axis and second-axis, and the electrical angle speed.