<p>The state of health (SOH) of lithium-ion batteries is critical to maintaining the stability and reliability of energy storage systems. To improve the accuracy of lithium-ion battery SOH prediction, a comprehensive prediction model integrating the Phototropic Growth Algorithm (PGA), a gated recurrent unit (GRU), and random forest (RF)-based residual correction was proposed. First, health indicators related to battery SOH were extracted from lithium-ion battery degradation data, and the gradient boosting decision tree (GBDT) algorithm was applied to select these health indicators as model inputs. Then, the PGA was adopted to optimize the hyperparameters of GRU to identify the optimal hyperparameter combination. Subsequently, the RF residual correction was applied to the predicted values output by the GRU. A dynamic correction weight was constructed by combining the 80% prediction interval width with the K-nearest neighbor (KNN)-estimated local prediction difficulty, which dynamically adjusts the RF correction intensity to obtain the final SOH prediction results of lithium-ion batteries. Validation experiments were carried out on the NASA and University of Maryland battery datasets, and the results demonstrate that the proposed method achieves high prediction accuracy and strong generalization performance.</p>