The practical application of time-variant reliability analysis is limited by its computationally expensive models which describe the structural system behavior. This paper presents a new adaptive PC-Kriging (APCK) approach to accurately and efficiently assess the time-variant reliabilities. Time interval is firstly discretized with a series of time instants and then the stochastic process is reconstructed by standard normal random variables and deterministic function of time. PC-Kriging (PCK) models are built at each time instant to predict the instantaneous responses of performance function. To improve the accuracy and efficiency, a new update strategy based on the integration of U- and H- learning functions is developed to refine the PCK models of instantaneous responses. One or two best samples are identified by the proposed learning criterion for updating the PCK models. Finally, Monte Carlo simulation (MCS) is used to estimate the time-variant reliability based on the updated PCK models. Four examples are used to validate the accuracy and efficiency of the proposed method.