The study of GNSS (global navigation satellite system) vertical time series is helpful for monitoring and analyzing the movement of crustal plates, and can provide an important basis for judging the movement trend. A MEMD-XGBoost model was constructed based on empirical mode decomposition and extreme gradient boosting algorithm for GNSS vertical time series prediction and analysis. In order to verify the prediction performance of the model, the vertical time series data of 8 GNSS stations were selected for prediction experiments. The feature construction results show that multiple empirical mode decomposition can accurately extract the original time series information and provide effective features. The modeling results show that the MEMD-XGBoost model can effectively improve the data quality. The prediction results show that the prediction results of the MEMD-XGBoost model have high precision and accuracy, and the degree of error dispersion is small, the model has strong stability and robustness, and can better predict the movement trend and seasonal changes in the U direction of the GNSS station. Therefore, the model can be applied to GNSS vertical time series modeling and prediction research.