The timely detection of anomalous flight behavior is critical to ensure a prompt and appropriate response to mitigate any dangers to flight safety or hindrance of logistics operations. Most previous approaches focused on anomaly detection, leading them to only be able to raise an alert after an occurrence of an anomaly. A more effective approach is to predict a potential anomaly based on current observations, thus cutting down on detection time and allowing for a more expedient response. We propose a novel martingale-based approach to predict anomalous flight behavior in the near future as data points are observed one by one in real-time. The proposed anomaly prediction method consists of two components: (i) utilization of regression to model the historical full flight behavior and (ii) monitoring of the real-time flight behavior using a martingale (stochastic) process. The latter component consists of two prediction steps: (i) first to predict future values of multiple target variables (e.g., latitude, longitude, and altitude) using regression models, and (ii) then to decide whether the predicted values exhibit anomalies. In particular, our proposed method uses martingale tests on multiple Gaussian process regression (GPR) predictive models of target variables. The main advantages of the proposed method are: (i) the use of multiple martingale tests allows one to have a tighter false positive bound for anomaly detection/prediction, and (ii) the prediction steps reduce the delay time for anomaly detection. Experimental results on real-world data show that the performance (mean delay time, recall, and precision) of our proposed approach is competitive against other compared methods.