Current state-of-the-art trajectory methods do not perform well in the terminal airspace that surrounds an airport due to its complex airspace structure and the frequently changing flight postures of aircraft. Since an aircraft that takes off or lands in an airport must follow a specified procedure, this paper will learn a data-driven trajectory prediction model from many historical trajectories to improve the accuracy and robustness of trajectory prediction in the terminal airspace. A regularization method is utilized to reconstruct each aircraft trajectory to obtain a high-quality trajectory with equal time intervals and no noise. Furthermore, we formulate the 4D trajectory prediction problem as a sequence-to-sequence learning problem, and we propose a sequence-to-sequence deep long short-term memory network (SS-DLSTM) for trajectory prediction, which can effectively capture the long and short temporal dependencies and the repetitive nature among trajectories. The proposed model is composed of an encoding module and a decoding module, where the encoding mode realizes the feature representation of historical trajectories, while the decoding module accepts the output of the encoding module as its initial input and recursively outputs the predicted trajectory sequence. The proposed method is applied to a dataset for the terminal airspace in Guangzhou, China. The experimental results demonstrate that our approach has relatively high robustness and outperforms mainstream data-driven trajectory prediction methods in terms of accuracy.