In the field of engineering structural reliability analysis, there are often implicit and highly nonlinear performance function issues. When using approximate analytical methods to estimate failure probability, the resulting calculations typically involve significant errors. Although numerical simulation methods can provide high-accuracy solutions for failure probabilities, they are hindered by excessively long computation times. Consequently, reliability analysis methods based on active learning Kriging models have gained widespread application in the reliability analysis of engineering structures. This paper, based on the classical U learning function, comprehensively considers the impact of sample point prediction values and prediction variances on the accuracy of failure probability estimation. In the sample space, priority is given to selecting sample points that are closer to the limit state surface, and higher weights are assigned to the prediction variances of these sample points. Based on this, a WU learning function is proposed. In constructing the WU learning function, the appropriate adaptive orientation function is determined by comparing the sample selection effectiveness of the WU function under various adaptive orientation functions. Furthermore, the AK-MCS-WU reliability analysis method is introduced in conjunction with the Kriging model. Two numerical examples and one engineering case demonstrate that the proposed AK-MCS-WU method can ensure the stable convergence of failure probability, while providing efficient and accurate predictions of structural failure probability for reliability problems involving complex performance functions.