Abstract: This study develops an efficient adaptive importancesampling method based on adaptive Markov chain Monte Carlo and fast Gausstransform technique for reliability analysis. In the proposed method, thesamples on the failure domain are generated by the adaptive Metropolisalgorithm, then the importance sampling density is constructed by means ofadaptive kernel density estimation method, and the fast Gauss transform arefinally adopted to accelerate the computation of the kernel function in theimportance sampling procedure. The adaptive Metropolis algorithm can obtainmore different samples on failure domain with the same computational effortwhen compared with the original Metropolis method. In another word, it caneffectively decrease the number of structural analyses and thereby canimprove the efficiency of the proposed method. The fast Gauss transform canconsiderably decrease the computational complexity of the kernel densityestimation method and avoid mounts of CPU time needed in the importancesampling procedure. Numerical examples illustrate that the proposed methodcan provide accurate and computationally efficient solutions of the problem.