Accurate prediction of the state of health (SOH) of power batteries was essential for extending the service life of new energy vehicles and ensuring driving safety. To address the limitations of BP neural networks in feature extraction, sensitivity to initial parameters, and local optima issues, a WPD-GA-BP-based prediction method was proposed. First, feature parameters were extracted using capacity increment analysis, and key features related to SOH were selected using Pearson correlation. Next, wavelet packet decomposition was applied to multi-scale reconstruct the label values, enriching the feature set. Finally, a genetic algorithm optimizes the BP neural network’s initial weights and thresholds, avoiding local optima and improving prediction accuracy. The results show that, compared to the pre-improvement WPD-BP and BP models, WPD-GA-BP reduces the maximum error to less than 1.5%, significantly improving prediction performance. It outperforms SVR and LSTM models, achieving the highest R2 and the smallest MAE and RMSE, demonstrating stronger accuracy and stability in predicting power battery SOH.