Abstract: Taking a power series polynomial model (PSPM) as a general nonparametric model of structural nonlinear restoring force (NRF), an iterative algorithm with strong tracking cubature Kalman Filter (STCKF) is proposed to identify structural mass, stiffness, damping parameters, and NRF of a nonlinear multi-degree-of-freedom (MDOF) structure, with the direct use of acceleration response measurement at limited degrees of freedom (DOFs). The effectiveness of the method proposed is numerically verified by a nonlinear MDOF structure involving different number of magnetorheological (MR) dampers with various parametric models for the purpose of mimicking various nonlinearity. The comparison is carried out between the results from the proposed approach and then using Updated Cubature Kalman Filter (UCKF), and higher identification accuracy of the method proposed is illustrated.