An efficient seismic fragility analysis (SFA) of unreinforced masonry (URM) buildings in the Bayesian framework utilizing limited numbers of nonlinear time history analyses (NLTHA) results is explored. Specifically, the SFA approach combines a generic Bayesian linear regression based demand prediction model with equivalent frame model based on advance force-based fibre elements to properly capture nonlinear seismic response of URM buildings. The effectiveness of the proposed approach is compared with the fragility results obtained by other commonly used SFA approaches considering the most accurate direct Monte Carlo Simulation (MCS) based results as the benchmark. The SFA approach is numerically demonstrated by considering a typical two storey URM building. The proposed SFA approach provides much improved fragility estimates using limited numbers of NLTHA results with respect to that of obtained by the other commonly used methods when compared with the direct MCS based fragility results.