Since the seismic damage can be concentrated within the interface between rocking members and good resiliency performance is observed，the rocking member draws more and more attention in seismic resistance and vibration reduction researches and engineering practices. In order to study the response of rocking pier subjected to different pulse-like excitations，the rocking response is analyzed based on different simplified excitations. Further，the key parameters are determined and analyzed. The rocking response results show that when the amplitude of single sinusoidal excitation increases，the free rocking pier is more likely to overturn. While，for the symmetric and antisymmetric Ricker function excitations without specified amplitude，as the excitation parameter，namely the size-frequency parameter，increases，the non-dimensional acceleration also increases. For the antisymmetric Ricker function，there is a flip at a large angle for its rocking response spectrum. It means that，at the initial stage，as the amplitude increases，the excitation frequency may be small instead. The displacement responses of the rocking pier under different seismic excitations are analyzed. Statistically，the difference between the displacements is small for large pier heights. Then，a design method based on the "equal displacement" rocking spectrum is proposed. Design example is also presented to prove the rationality of the proposed method. Further，it provides theoretical support for the design of such kinds of rocking members.