In this study, the recursive update algorithm of subspace system identification is proposed for estimating dynamic characteristics of a time-varying multi-input multi-output (MIMO) building structure using the pastinput/ output multivariable output-error state space (PO-MOESP) based algorithm. First, the recursive subspace identification with Bona-fide LQ renewing algorithm (RSI-BonaFide-Oblique) incorporated with moving window technique is utilized to identify modal parameters such as natural frequencies, damping ratios and mode shapes at each time instant during the strong earthquake excitation, which assumes the equivalent linear dynamic characteristic in every moving time window with a fixed length. In addition to identifying the instantaneous dynamic characteristics of the structural system using RSI, several damage detection algorithms related to the reconstructed system stiffness matrix using simplified model was derived from the previously identified modal parameters to quantify the damage extent, specify its corresponding damage location, the time of occurrence during the excitation, and the percentage of stiffness reduction. To demonstrate the capability of the proposed recursive subspace identification algorithm and the damage assessment technique, dynamic response data generated from a shaking table test of a two 3-story steel structure experiment is used to verify the algorithms on detecting damage caused by nonlinear behavior occurring on the steel column. Besides, a building seismic response data (collected from Chi-Chi earthquake) was also used to evaluate the damage situation during severe earthquake excitation.