Some major key structures will face extreme events during their service life, which may be ignored due to their extremely low probability, but will result in serious losses if they occur. In order to accurately estimate the minimum probability of failure of complex structures, this paper presents a method that can balance the accuracy and cost of calculating the probability of extreme events. Using an active learning strategy based on a Gaussian surrogate metamodel, a search function is constructed that can effectively concentrate the training points on one side of the tail, and the function is better at finding the maximum error region weighted by the distribution function and re-investing the new training points. To verify the effectiveness of the algorithm, the nonlinear analysis of a structural crack is taken as an example. The relative error of the proposed algorithm is about 10% compared to MCS. The mean relative error of the estimated random variables is about 10%, indicating that this method can obtain acceptable statistical results. Compared to the results of AL-GP, the error expectation of the estimated random variables is reduced by 20%, indicating that the uncertainty in the tail can be reduced faster. The example proves that the algorithm is more sensitive to the tail and is suitable for the distribution calculation with potential tail risk.