According to a typical structure of non-resonant elliptical vibration cutting (EVC) device, the dynamic hysteresis characteristics of piezoelectric stack in non-resonant EVC device are considered, the static PI hysteresis model is segmented into dynamic weights, and the dynamic PI hysteresis model is constructed to describe the relationship between the axial input voltage and the output displacement of the non-resonant EVC device. The feed-forward controller of the non-resonant EVC device is established by inversion of the hysteresis model, and in order to further improve the accuracy and stability of the control system, the PID feedback link is introduced and the feed-forward is used. The compound control method of inverse controller and PID feedback is used to control the sinusoidal displacement of the specified frequency and amplitude of each axial output of the non-resonant EVC device, so that the motion frequency, shaft length and inclination of the elliptical vibration track can meet the requirements, and the non-resonant EVC device can be controlled. The experimental results show that the non-resonant EVC device can output an elliptical vibration trajectory with an adjustable amplitude and dip angle below 100Hz under compound control, and the motion error is less than 3.5%.