The rapid growth of civil aviation has posed significant challenges to air traffic management (ATM), highlighting the need for accurate aircraft trajectory prediction (TP). Due to the scarcity of relevant data and the resulting class imbalance in the sample, aircraft TP under severe weather conditions faces significant challenges. This paper proposes an aircraft TP method framework consisting of trajectory data augmentation and TP networks to address this issue. To validate the effectiveness of this framework in solving the TP problem in severe weather, we propose an improved conditional tabular generative adversarial networks (CTGAN)-long short-term memories (LSTMs) hybrid model. We conduct comparative experiments of four LSTM-based models (LSTM, convolutional neural network (CNN)-LSTM, CNN-LSTM-attention, and CNN-BiLSTM) under this framework. The improved CTGAN is also compared with the commonly used data augmentation method, the Synthetic Minority Oversampling Technique (SMOTE). The results show that the TP accuracy can be effectively improved by enhancing the minority-class sample data; compared with SMOTE, the improved CTGAN is more suitable for minority-class sample data augmentation for aircraft TP, and it also shows that for minority-class sample data augmentation, data distribution characteristics are more important than the simple trajectory point accuracy. The hybrid modeling approach with the improved CTGAN as the data augmentation network proposed in this study provides valuable insights into addressing the data imbalance problem in aircraft TP.