Abstract: To meet the seismic design requirements of a self-centering system in near fault area, and to reveal the elastoplastic performance of structures under seismic excitations, the C_DI (constant-damage displacement spectra) of a self-centering system was established based on the Park-Ang damage model. The results were statistically organized to evaluate the influence of damage model parameters and hysteretic model parameters on C_DI. The differences of an inelastic displacement spectra based on constant-damage approach and constant-ductility approach, and the differences of C_DI corresponding to near-fault pulse-like and non-pulse-like ground motions were compared and analyzed. A prediction equation was proposed to estimate C_DI of the self-centering system. Results show that: the period normalization with respect to pulse period can reflect the local amplification effect of the pulse characteristic on the values of C_DI in the short period range, and effectively reduce the dispersion of C_DI. The influence of ultimate ductility coefficient on the values of C_DI is more than 20% in the short period range. The comparative analysis of C_DI and C_μ (constant-ductility displacement spectra) shows that the effect of cumulative hysteretic energy dissipation on displacement demand of self-centering systems cannot be ignored. In comparison with no-pulse-like ground motions, near-fault pulse-like ground motions can significantly increase the values of C_DI at the normalized period around 0.5 and 1.0, and magnitude of increase can reach about 20%. The proposed prediction equation can be applied to anticipating the displacement response of self-centering systems in near fault area.