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Predicting flight trajectories is a research area that holds significant merit. In this paper, we propose a data-driven learning framework that leverages the predictive and feature extraction capabilities of the mixture models and seq2seq-based neural networks while addressing prevalent challenges caused by error propagation and dimensionality reduction. After training with this framework, the learned model can improve long-step prediction accuracy significantly given the past trajectories and the context information. The accuracy and effectiveness of the approach are evaluated by comparing the predicted trajectories with the ground truth. The results indicate that the proposed method has outperformed the state-of-the-art predicting methods on a terminal airspace flight trajectory dataset. The trajectories generated by the proposed method have a higher temporal resolution (1 time step per second vs 0.1 time step per second) and are closer to the ground truth.