Bayesian Approach for efficient collapse response assessment of structure is used in this study. The approach facilitates integration preliminary information of risk assessment with numerical analysis results to get more efficient fragility assessment. We can get the preliminary information from different sources, including professional experience, information on the building design criteria, experimental results and simplified linear dynamic analysis. The combination of prior collapse risk information with nonlinear analysis simulations aims to improve computational and statistical efficiency. In this study, we considered a 62m cantilever and independent intake tower to assess its seismic fragility. The approach provides significant improve the statistical and computational efficiency of seismic fragility as well as precise confidence band of fragility curve compared to alternative method.