This study presents a combined Long Short-Term Memory and Extreme Gradient Boosting (LSTM-XGBoost) method for flight arrival flow prediction at the airport. Correlation analysis is conducted between the historic arrival flow and input features. The XGBoost method is applied to identify the relative importance of various variables. The historic time-series data of airport arrival flow and selected features are taken as input variables, and the subsequent flight arrival flow is the output variable. The model parameters are sequentially updated based on the recently collected data and the new predicting results. It is found that the prediction accuracy is greatly improved by incorporating the meteorological features. The data analysis results indicate that the developed method can characterize well the dynamics of the airport arrival flow, thereby providing satisfactory prediction results. The prediction performance is compared with benchmark methods including backpropagation neural network, LSTM neural network, support vector machine, gradient boosting regression tree, and XGBoost. The results show that the proposed LSTM-XGBoost model outperforms baseline and state-of-the-art neural network models.