To tackle the intricate challenges of nonlinearity and non-stationarity in lead-acid battery degradation data, this paper introduces the SG-LSTM model, an innovative approach to battery health prediction. This model uniquely integrates Singular Spectrum Analysis (SSA) and Grey Wolf Optimization (GWO) with Long Short-Term Memory (LSTM) networks, forming a sophisticated predictive framework. By targeting key degradation features, such as the charging time of multiple voltage rise segments from the charging curve, the model effectively captures critical battery health dynamics. SSA plays a vital role by filtering outliers from these feature sequences, ensuring high-quality data for analysis and enhancing the robustness and accuracy of predictions. The refined data are then processed by a GWO-optimized LSTM network, where GWO’s bio-inspired optimization fine-tunes the LSTM parameters for optimal performance. Experimental results demonstrate that the SG-LSTM model outperforms existing models in prediction accuracy and stability; specifically, SG-LSTM achieves 0.27 RMSE, outperforming LSTM (0.84), SSA-LSTM (0.4), and SSA-BP (0.6).