A positioning controlling device for improving the machineing accuracy of a work of a non-circular shape. A control axis is driven in accordance with an input function consisting of position instruction data corresponding to a machining shape of a work, and a response function of the position of the control axis is measured actually. Then, a transfer function of the servo system is determined from Fourier transformation of the input function and Fourier transformation of the response function, and a corrected input function with which a response function of the control axis ideally corresponds to the machining shape of the work is obtained from the transfer function. Even if the control axis is driven in accordance with the corrected input function, a response function obtained does not correspond to the ideal machining shape of the work. Therefore, the calculations for obtaining an input function described above are sequentially executed until a response function obtained converges to the ideal machining shape. As a result, even if the servo system has a non-linearity, if the control axis is controlled in accordance with an input function finally obtained in this manner, then a response function then corresponds to the ideal machining shape.