Taking a mid-span continuous bridge as the research subject, the restoring force model of rubber bearing and the dynamical model of nonlinear analysis were established. Also, 100 earthquake wave records were chosen from PEER to conduct a series of nonlinear time-history analyses, and the relative displacement responses of rubber bearings were obtained. Based on the principle of Performance-Based Seismic Design and the theory of seismic vulnerability analysis, a method for determining four different damage indexes of laminated rubber bearing was proposed. According to traditional reliability probability analysis method, a curve between the spectral acceleration and the relative displacement ductility ratios of bearings was fitted, and the fragility curves of different bearings were formed. The results have demonstrated that bearing, especially the bearing on abutment, is more vulnerable than other bridge members under earthquake. Therefore, the seismic performance of bearing will be greatly improved if the thickness of rubber bearings is heightened or the PTFE sliding rubber bearings are adopted for abutment bearing.