To develop an accurate and effective short-term air traffic flow prediction model to improve the efficiency of terminal area management, the arrival traffic flow was chosen as the research subject. Firstly, the ARMA(autoregressive moving average) model was adopted for initial linear prediction of the flow time series. Then, the residual sequence after linear prediction was subjected to non-linear correction using the LSTM(long short term memory) model. To address the issue of decreased prediction accuracy caused by redundant features, the AE(autoencoder) model was used to adaptively compress and optimize the input of weather and traffic flow features for the LSTM model. Finally, a comparative experiment was conducted to validate the accuracy, robustness, and timeliness of the ARMA-AE-LSTM model. Experimental results demonstrate that the proportion of predicted absolute errors within 1.3 aircraft reaches 75%. The average iteration time of the LSTM model is reduced to 1.014 seconds. When compared with other commonly used deep learning prediction models, the ARMA-AE-LSTM model improves the RMSE(root mean square error), MAE(mean absolute error), and R²(r-squared) evaluation metrics by 45.98% ~ 67.66%, 48.56% ~ 67.35%, and 5.18% ~ 21.07%, respectively. Furthermore, the ARMA-AE-LSTM model exhibits better robustness in adverse weather conditions. Thus, it can be concluded that this method enables accurate, effective, and rapid prediction of air traffic flow.