The main task of structural reliability analysis is to estimate failure probability of a studied structure taking randomness of input variables into account. To consider structural behavior practically, numerical models become more and more complicated and time-consuming, which increases the difficulty of reliability analysis. Therefore, sequential strategies of design of experiment (DoE) are raised. In this research, a new learning function, named least improvement function (LIF), is proposed to update DoE of Kriging based reliability analysis method. LIF values how much the accuracy of estimated failure probability will be improved if adding a given point into DoE. It takes both statistical information provided by the Kriging model and the joint probability density function of input variables into account, which is the most important difference from the existing learning functions. Maximum point of LIF is approximately determined with Markov Chain Monte Carlo(MCMC) simulation. A new reliability analysis method is developed based on the Kriging model, in which LIF, MCMC and Monte Carlo(MC) simulation are employed. Three examples are analyzed. Results show that LIF and the new method proposed in this research are very efficient when dealing with nonlinear performance function, small probability, complicated limit state and engineering problems with high dimension. (C) 2016 Elsevier Ltd. All rights reserved.