The seismic performance of a fully fabricated bridge is a key factor limiting its application. In this study, a fiber element model of a fabricated concrete pier with grouting sleeve-prestressed tendon composite connections was built and verified. A numerical analysis of three types of continuous girder bridges was conducted with different piers: a cast-in-place reinforced concrete pier, a grouting sleeve-fabricated pier, and a grouting sleeve-prestressed tendon composite fabricated pier. Furthermore, the seismic performance of the composite fabricated pier was investigated. The results show that the OpenSees fiber element model can successfully simulate the hysteresis behavior and failure mode of the grouted sleeve-fabricated pier. Under traditional non-near-fault ground motions, the pier top displacements of the grouting sleeve-fabricated pier and the composite fabricated pier were less than those of the cast-in-place reinforced concrete pier. The composite fabricated pier had a good self-centering capability. In addition, the plastic hinge zones of the grouting sleeve-fabricated pier and the composite fabricated pier shifted to the joint seam and upper edge of the grouting sleeve, respectively. The composite fabricated pier with optimal design parameters has good seismic performance and can be applied in high-intensity seismic areas; however, the influence of pile-soil interaction on its seismic performance should not be ignored.