With ahead-of-time aircraft management, we are able to reduce aircraft collision and improve air traffic capacity. However, there are various impact factors which will cause a large deviation between the actual flight and the original flight plan. Such uncertainty will result in an inappropriate decision for flight management. In order to solve this problem, most of the existing research attempt to build up a stochastic trajectory prediction model to capture the influence of the weather. However, the complexity of the weather information and various human factors make it hard to build up an accurate trajectory prediction framework. Our approach considers the problem of trajectory deviation as the "anomaly" and builds up an analytics pipeline for anomaly detection, anomaly diagnostics, and anomaly prediction. For anomaly detection, we propose to apply the CUSUM chart to detect the abnormal trajectory point which differs from the flight plan. For anomaly diagnostics, we would like to link the entire anomalous trajectory sequences with the convective weather data and extract important features based on time-series feature engineering. Furthermore, XGBoost was applied to detect the anomalous trajectory sequences based on the time-series features. For anomaly prediction, we will build up a point-wise prediction framework based on the Hidden Markov Model and Convectional LSTM to predict the probability that the pilot would deviate from the flight plan. Finally, we demonstrate the significance of the proposed method using real flight data from JFK to LAX.