Bayesian model updating provides a powerful and comprehensive framework for engineers to assimilate up-to-date observation data into models based on probability theory and significantly reduces model uncertainties. By integrating the concept of population Monte Carlo within the cross-entropy method, a novel adaptive importance sampling (AIS) algorithm is recently proposed to conduct robust and fast model updating using Gaussian mixture. This algorithm has been proved to enable constructing an importance sampling density (ISD) that mimics the target posterior density and is adopted in this paper to tackle a seismic analyses problem of 1-story moment frame with viscous damper. Results showcase that the distributions of parameters can be successfully updated using the algorithm with low computational cost. The updated results can also be further leveraged to guide the seismic safety assessment.