In order to improve the shear resistance and structural ductility of the perfobond rib (PBL) connector, a new PBL connector with steel–rubber tenon is proposed in this study, which aims to increase the shear load capacity of the connector while improving the ductility of the connector. First, models of new PBLs are established based on the validated finite element method, and their mechanical properties are compared with other shear connectors. The results show that the stiffness and shear load capacity of the proposed connector can be effectively improved when the steel ring is added, where the shear stiffness can be reduced, and the deformation capacity of the specimen can be improved when the rubber ring is added. When a steel ring with a thickness of 5 mm and a rubber ring with a thickness of 5 mm are involved, the shear load capacity of the connector with steel–rubber tenon is increased by 13.7%, and the shear stiffness is reduced by 37.3% compared to the conventional concrete tenon connector, while the ductility is increased by 75.1% compared to the connector with steel ring tenon. Subsequently, as for the connectors with steel–rubber tenon, the effects of the thickness of the steel ring, the thickness of the rubber ring, the diameter of perforated rebar, the strength of concrete and the strength of perforated steel plate are analyzed based on the finite element model of a PBL. The results show that an increase in the thickness of the steel ring, the diameter of the perforated rebar and the strength of the concrete will cause an increase in the shear stiffness and shear load capacity of the connector; however, an increase in the thickness of the rubber ring can cause a decrease in the shear stiffness and shear load capacity of the connector, while a change in the strength of perforated steel plate has little effect on the shear stiffness and shear load-carrying capacity. Finally, based on the finite element parametric analysis results and the damage mechanism of the proposed connector, a calculation equation applicable to the PBL connector with steel–rubber tenon is presented to predict the shear load capacity of the connector.