Abstract: The probability density evolution method demonstrates good applicability for system reliability analysis of complex engineering structures. However, it still faces a lot of challenges, such as inefficiency, particularly when dealing the reliability issues with high-dimensional stochastic dynamic systems. In recent years, a promising approach to enhance the efficiency of reliability analysis involves training surrogate models using a small set of training samples instead of relying on the actual stochastic system is favored by researchers. To improve the accuracy and efficiency of constructing adaptive surrogate models in order to carry out the system reliability analysis, this paper proposes a two-phase adaptive training strategy based on the adaptive Kriging model. It involves hierarchical partitioning of the probability space to obtain training sample sets at different levels. Building on this two-phase training strategy, the Kriging model is trained step by step. This not only enhances the Kriging model's approximation accuracy of failure boundaries within the probability space but also reduces the computational memory requirements during the training process. Subsequently, by combining the probability density evolution theory, an efficient reliability analysis method based on equivalent extreme value event is introduced. To validate the effectiveness of the proposed method, the construction of surrogate models for different types of performance functions is analyzed, and seismic reliability analysis of a reinforced concrete frame structure is conducted. The results indicate that the two-phase adaptive training strategy greatly improves the derivation rate of the objective surrogate model while maintaining high analysis accuracy, addressing the shortcomings of the probability density evolution theory in dealing with rare failure events. It is worth mentioning that the two-phase training strategy is not only suitable for surrogate model training based on the Kriging model, but also has guiding significance for the training of other types of adaptive surrogate models, and is not limited by the basic type of surrogate model.