Based on the impact phenomenon between the end of the beam and the bridge abutment of the curved continuous bridge during earthquakes, a spatial finite element calculating model with collision element is presented. The law of collision is studied by the nonlinear contact time history analysis method under two three-dimensional ground motions. The variation laws of relative displacement and the internal force at the bottoms of piers are researched. In addition the changing of displacement and internal force at the end diaphragm are studied. The results show that the pounding action can easily lead to significant collision forces between the end beam and the abutment of the curved bridge which increases the axial force of girder evidently. The collision forces and longitudinal displacements from the inner to outer of the diaphragm generally are showed by an increasing trend, and the pounding action is more fierce under Elcentro ground motion than that under Tianjin ground motion.There is no relative displacement of consolided pier, bending moment and shear force of the consolided pier are greater than that of the mobile pier.The conclusions from the present study may serve as a reference base for seismic design of continuous curved bridges.