A double-column self-centering pier fused with shear links is a novel structure developed to reduce residual deformation and facilitate post-earthquake repair. With this novel structure, the seismic resilience of bridges can be improved, and the reliability of lifeline infrastructure can be ensured. This paper presents the proposed pier configuration and investigates the mechanical behavior of the pier. A simplified finite element model is established to develop the lateral force-displacement relationship under cyclic loading. Additionally, a theoretical model based on the matrix displacement method and the virtual work principle is proposed to calculate the lateral force-displacement skeleton curve. The rationality and reliability of the theoretical model are validated by the satisfactory agreement observed between the numerical and theoretical results. Furthermore, a series of parametric analyses are conducted to discuss the effects of key parameters. The outcomes of this work can serve as a reference for further development of the design method for the innovated pier.