Abstract: For the implicit limit state function usually encountered in an engineering reliability analysis and design, the Support Vector Machine (SVM) reliability analysis method is proposed on fast Markov chain simulation. In the proposed method, Markov chain is used to simulate the samples in the importance region defined by the limit state function, and the surrogate model is obtained by using these samples to train a SVM. Since Markov chain can adaptively simulate the samples of the importance region, and the candidate states but not Markov states are used as the training samples, the proposed method can well approximate the limit state equation in the region contributing to the failure probability significantly, and can utilize the information provided by Markov chain simulation sufficiently. In addition, the gradual change on variance in a simulation process is adopted to improve the quality of the Markov chain samples. Moreover, the proposed method uses the SVM regression method and classification method to construct the surrogate model, which can minimize the risk in approximating the limit state equation, and thus approximate the failure probability with a high precision. Finally numerical and engineering examples illustrate that the proposed method owns good performance in calculating efficiency and precision.