The real-time risk assessment is critical for the decision making and the safety of the National Airspace System (NAS). The adaptive kriging model has the benefit that it can achieve accurate results compared with the sample-based method such as Monte Carlo simulation but with less training data. That is used to develop a framework for the efficient risk assessment (both time-independent and time-dependent problems) in NAS. The framework can be used to the problems with different types of uncertainties and multiple well-defined safety metrics. The efficiency and accuracy of the methods are demonstrated by case studies of risk assessment loss of separation and hazardous weather avoidance.