Reliability measures the ability that the structure finishes its intended function without failures by taking uncertainties into account. Reliability sensitivity commonly is defined as the partial derivative of the failure probability with respect to the distribution parameter, which is often of great importance for the reliability-based design optimization. In this paper, two improvements and one extension of the subdomain sampling (SS) method are researched. The first improvement is the criterion for adaptively determining the number of subdomains. The second improvement is that based on the first improvement, adaptive Kriging (AK) model is embedded into the modified SS (MSS) method to substitute the actual limit state function to identify the limit states of the samples generated in the MSS method. Through adaptively partitioning the distribution region, the size of candidate sampling pool in each circle of updating process of Kriging model is decreased compared with that in the method with the candidate samples being directly sampled in the whole uncertain distribution region, which improves the efficiency of each circle’s updating process. Then, the MSS-based adaptive Kriging (AK-MSS) method is extended to the reliability sensitivity analysis where no extra model evaluations are needed after the failure probability is assessed by the AK-MSS method. That is to say, the reliability and the reliability sensitivity can be simultaneously estimated by the AK-MSS method. Results of case studies in this paper demonstrate the effectiveness of the AK-MSS method.