Abstract: To improve the seismic performance of outriggers in super-tall buildings and to eliminate the defects of obvious strength and stiffness degradation, low energy dissipation and large residual deformation after the buckling of conventional diagonal members, a self-centering viscoelastic diagonal member (SC-VEDM) with stable initial stiffness, high energy dissipation and self-centering capacity is designed to replace conventional steel diagonal members. This component is assembled by viscoelastic materials, prestressed tendons and shaped steels with proper configuration measures. The energy dissipation capacity is provided by the shear deformation of the viscoelastic material whereas the self-centering capacity is provided by the tension in the prestressed tendons. A theoretical mechanical model of the SC-VEDM is established. The stress characteristics at different work stages as well as a theoretical restoring force model are analyzed. The hysteresis performance of the SC-VEDM is predicted by a fine finite element model with MSC.Marc software. The results show that the proposed configuration measures of SC-VEDM are feasible and that the SC-VEDM has stable initial stiffness, high energy dissipation and self-centering capability. Good agreement of hysteretic curves between the simulation and theoretical results is observed. The relative deviation of the first stiffness is approximately 0.4%, the maximum relative deviation of compressive strength is approximately 4.64%, and the maximum relative deviation of energy dissipation capacity is approximately 10.9%. The model lays the foundation for subsequent experiment and design method research of SC-VEDM.