Steel plate shear wall (SPSW) systems are utilized in steel structures as a lateral-force-resisting system in high seismicity zones. In conventional SPSW systems, the stiffness and energy absorption mechanisms are combined in the main structural members, resulting in the formation of inelastic deformations, severe damages, and residual lateral displacements. Therefore, a combination of SPSW systems with passive dampers is employed to mitigate these defects. This study numerically investigates the seismic behavior of a new lateral-force-resisting system, which combines a viscoplastic damper and steel plate shear wall. The proposed damper is constituted of a layer of high-damping rubber with viscoelastic and hyperelastic characteristics and ductile steel bolts. The suggested SPSW systems can improve structural resilience, including damage control, self-centering behavior, and building performance levels. Once the results of numerical analyses were validated with the experimental works, several nonlinear finite element models were used to evaluate the overall seismic response of the proposed system. The results showed that the proposed damper could perform as a fuse, protecting the main structural elements to be elastic and undamaged. In addition, the high-damping rubber could substantially reduce the residual lateral displacements and improve the self-centering behavior compared to the conventional SPSW systems.