In order to fully explore the time dependence of aircraft trajectory within airport terminal areas and solve the problem of unstable medium and long term and multi-step trajectory prediction accuracy, an attention mechanism and exponential decay sampling method in teacher forcing were introduced, and a Seq2Seq-attention mechanism-exponential decay (SAE) model for airport terminal area trajectory prediction based on the Seq2Seq framework was proposed. The Seq2Seq framework achieves multi-step prediction, attention mechanism improves decoder prediction accuracy, exponential decay sampling method accelerates model convergence during the training phase, and to some extent improves model generalization. Finally, in order to verify the effectiveness of the proposed method, the original data set was constructed using the ADS-B trajectory data of 28 aircraft and 90 days in Tianjin Terminal Area, and the mean absolute error (MAE) and root mean square error (RMSE) were used as model performance evaluation indicators to carry on aircraft trajectory prediction experiments. The experimental results show that the recurrent neural network of altitude, longitude and latitude within the Seq2Seq framework utilizing LSTM, GRU and LSTM can achieve the best predictive performance. Four prediction windows of 1, 3, 5 and 10 min were used for modeling. Compared with the results with the best prediction performance in the baseline model, the proposed method performed best in the altitude, longitude and latitude indicators on the verification set. MAE under the 10 min prediction window is reduced by 66.30%, 54.62% and 36.59%, and RMSE is reduced by 65.45%, 38.16% and 20.57%, respectively. At the same time, the mean and variance of the proposed method's prediction results are the smallest under the four prediction durations mentioned above, indicating that as the prediction duration increases, the stability of the model's prediction results is the best. In addition, the attention mechanism and exponential decay sampling method introduced have a positive contribution to effectively capturing trajectory time dependence and improving model generalization.