The spectral displacement and the damage state medians were assumed as deterministic parameters in HAZUS-Advanced Engineering Building Module (AEBM). As the historical material and experimental data were insufficient to establish an exactly probability density function model of uncertain variable, the damage assessment results by probabilistic model derived from many assumptions and simplification were unreliable. The uncertainties of the spectral displacement and damage state medians were modeled by the Envelope Bound Convex Model. Furthermore, a bound fragility analysis methodology is derived by integrating HAZUS-AEBM module with the convex set theory. The fragility of a hotel in southern China are calculated and compared to the damage derived by HAZUS-AEBM method, and the results of fragility analysis are more sensitive to the spectral displacement and the damage state medians.