Abstract: The analysis of dynamic responses of a reinforced concrete pier with eccentricity based on fiber unit model under strong earthquake was carried out.Through the analysis of damage status of section, residual deformation, the time history of deformation and the strain time history of concrete, the characteristic of the eccentric pier was discussed, when very large one-way deformation and residual deformation occurred in the direction of beam cantilever.It was pointed out that the direction should be considered even if the unidirectional seismic wave was inputted while analyzing the earthquake response of eccentric piers, the input of bidirectional earthquake wave had a great influence on residual deformation.