Accurate remaining useful life (RUL) prediction for lithium-ion batteries is crucial for battery health monitoring and early fault warning systems. This paper proposes a comprehensive predictive framework that integrates ICEEMDAN, XGBoost, and the deep learning model Transformer. This method first utilizes the ICEEMDAN technique for efficient multi-scale decomposition of battery capacity degradation data, extracting intrinsic mode functions (IMFs) that reflect local capacity fluctuations and a residual sequence (RES) that indicates the overall degradation trend. Subsequently, the XGBoost algorithm assesses the relationship between each IMF and RES component and the battery capacity degradation, assigning appropriate weights for subsequent predictions. Finally, the Transformer model independently predicts each component and combines these predictions, weighted by the XGBoost evaluation, to achieve a more accurate RUL prediction. Using aging experiment data from different batteries, the performance of the ICEEMDAN-XGBoost-Transformer model is compared with that of the ICEEMDAN-Transformer and Transformer models. Results indicate that this method offers high prediction accuracy, with average capacity prediction errors of RMSE, MAPE, and MAE being 0.01834, 0.02164, and 0.01319, respectively. When the prediction starting point is set at cycle 40, the absolute error in RUL prediction is less than 7 cycles, outperforming other similar models.