Considering the influence of large deformation, the non-linear dynamic equations of a high pier under the foundation ellipse motion caused by Rayleigh wave by earthquake were established. By supposing the displacement shape function and applying the Galerkin method, the dynamic equations about time were obtained. By processing numerical calculation, the displacement response curves of the high pier under the foundation ellipse motion with different magnitude and the overall process from the transverse vibration to the instability of the high pier were given. The critical seismic acceleration and the instability time were obtained. The influence of different seismic peaks, the slenderness ratio and the weight of the bridge on the displacement response, the critical seismic acceleration and the instability time were analyzed.