In practical engineering applications, reliability analysis may involve both random variables and interval variables owing to limited information. In addition, reliability exhibits a distinct time-variant effect due to material property degeneration and dynamic load processes. Most of the current methods, however, are only capable of dealing with the hybrid time-invariant reliability analysis, and cannot ensure the high reliability level during a product life-cycle. This paper proposes a new method, referred to as active learning Kriging-mixed optimization (ALK-MO), which can efficiently and accurately tackle hybrid time-variant reliability issues with mature probabilistic tools. The key of ALK-MO is to construct an extreme response surface (ERS) of the performance function by employing Kriging model. Mixed optimization (MO) algorithm, which draws samples of time, random variables and interval variables simultaneously, is used to obtain the data for the ERS efficiently. Based on the active learning theory, an automatic updating mechanism is developed to gradually improve the accuracy of the ERS by adding the best random samples. With ALK-MO, the hybrid time-variant reliability analysis can be converted into the probabilistic time-invariant reliability analysis and existing mature reliability analysis methods can be used. The proposed method is applied to a mathematical example and an engineering example. The results shows that ALK-MO is efficient and accurate, and has a good prospect of engineering application.