Abstract: A nonlinear restoring force describes directly the initiation and development procedure of structural damage under dynamic loadings and, strictly speaking, the conventional structural identification approaches based on eigenvalue or eigenvector extraction are not applicable for nonlinear dynamic systems due to the nonlinearity accompanying with the damage initiation and development. In this study, a Chebyshev polynomial model based on structural dynamic response time series is proposed to model the nonlinear restoring forces under complete and incomplete excitation scenarios. Without the use of any assumption on the nonlinear restoring model and mass distribution, the nonlinear restoring force is identified by the least square method under different excitation conditions. The feasibility and robustness of the proposed approaches were illustrated via numerical simulation with a multi-degree-of-freedom (MDOF) structure equipped with a magneto-rheological (MR) damper considering the effect of noise and dynamic test measurements with a 4-story steel frame equipped with two MR dampers to mimic structural nonlinear performance. Identification results are compared with that of the previously proposed power polynominal based approach. The results show that the proposed approach identifies the nonlinear restoring force with higher accuracy and provides a way for the damage initiation and development procedure monitoring and for the quantitative energy consumption evaluation of engineering structures under strong dynamic loadings.