Accurately predicting the remaining useful life (RUL) of lithium batteries is crucial for ensuring reliable equipment operation, mitigating safety risks. This is of great significance for advancing the new energy industry. To improve the adaptability of grey model to the lithium battery aging process, a recursive least-squares parameter estimation method is incorporated into the non-homogeneous grey model. By incorporating the latest operational data from lithium batteries in real time, the model parameters are updated recursively, effectively tracking the dynamic patterns of lithium battery aging. This paper validates the proposed model using the University of Oxford’s public lithium battery dataset. To address the issue of sudden capacity failure in lithium batteries, we propose an online abnormal detection method based on sliding window residual statistics and modify the recursive non-homogeneous grey model. The results indicate that this proposed model can accurately predict the remaining useful life of lithium batteries, demonstrating good predictive accuracy and stability. It is capable of meeting the requirements for predicting the RUL of lithium batteries in practical engineering applications