A relevance vector machine (RVM) based demand prediction model is explored for efficient seismic fragility analysis (SFA) of a bridge structure. The proposed RVM model integrates both record-to-record variations of ground motions and uncertainties of parameters characterizing the bridge model. For efficient fragility computation, ground motion intensity is included as an added dimension to the demand prediction model. To incorporate different sources of uncertainty, random realizations of different structural parameters are generated using Latin hypercube sampling technique. Mean fragility, along with its dispersions, is estimated based on the log-normal fragility model for different critical components of a bridge. The effectiveness of the proposed RVM model-based SFA of a bridge structure is elucidated numerically by comparing it with fragility results obtained by the commonly used SFA approaches, while considering the most accurate direct Monte Carlo simulation-based fragility estimates as the benchmark. The proposed RVM model provides a more accurate estimate of fragility than conventional approaches, with significantly less computational effort. In addition, the proposed model provides a measure of uncertainty in fragility estimates by constructing confidence intervals for the fragility curves.