This article describes a new adaptive Kriging method designed to alleviate the limitations of other related approaches encounter in cases of extremely rare failure events. The main idea is to iteratively reduce both surrogate modelling error and sampling error. To do so the adaptive Kriging framework is associated with the multiple adaptive importance sampling scheme where the auxiliary distribution is iteratively built as a near optimal Gaussian mixture. The estimator associated with he Gaussian mixture importance sampling is given as well as a stopping criterion based on both the estimated sampling and modelling error. The performances are finally illustrated on two benchmark problems.