•Stratified importance sampling and adaptive Kriging are combined for reliability analysis.•Importance sampling density is constructed through an adaptive Kriging method.•Variable for stratification is chosen based on Kriging surrogate to decrease the cost.•Numerical and practical examples show the efficiency of the proposed method. In reliability engineering, estimating the failure probability of a system is one of the most challenging tasks. Since many applied engineering tasks are computationally expensive, it is challenging to estimate failure probabilities using acceptable computational costs. In this paper, to reduce computational cost, we combine a stratified importance sampling method with an adaptive Kriging strategy to estimate failure probabilities. Compared to the importance sampling method, stratified importance sampling needs fewer samples to get an estimate of failure probability with the same coefficient of variation. In the proposed method, we improve the importance sampling density and determine the best input variable for stratification through a Kriging-based model surrogate technique (like a Gaussian process regression). Then, the Kriging surrogate is further adaptively improved to get an accurate estimate of failure probability. The efficiency of the proposed method is demonstrated using several analytic examples and then transferred to a carbon dioxide storage benchmark problem.