This paper proposes a generalized hybrid reliability analysis (HRA) method under probability and interval uncertainties by a two-stage active learning Kriging (TALK) model. The proposed TALK-HRA method can deal with the probability and interval model, interval-probability model, as well as their combination. A first-stage active learning Kriging model is first established to represent the separator determining sign of performance functions locally. Then, a second-stage Kriging model is further constructed to approximate the region of interest around the maximal or minimal failure probability. The detailed principles of the proposed method are further provided to efficiently and accurately calculate the upper and lower bounds of the failure probability. The possible application to random-fuzzy reliability analysis is also discussed. Finally, five numerical examples are investigated to demonstrate the validity of the proposed method. The results show that the proposed method can be well applicable to the HRA of ‘black box’ problems with high nonlinearity as well as multi-peak limit state surface.