Accurate State of Health (SOH) estimation of lithium-ion batteries (LIBs) is critical for ensuring the safety of electric vehicles and improving the reliability of battery management systems (BMS). However, the use of individual health features (HFs) and the selection of hyperparameters can increase the data processing burden on the BMS and reduce the accuracy of data-driven models. To address the above issue, this paper proposes a novel SOH estimation method for lithium-ion batteries based on the PSO–GWO–LSSVM prediction model with multi-dimensional health feature extraction. To comprehensively capture the battery aging mechanisms, four categories of health features—time, energy, similarity, and second-order features—are extracted from the LIBs charging segments. The correlation between HFs and SOH is comprehensively evaluated through Pearson and Spearman correlation analyses, followed by Gaussian filtering and outlier detection to enhance feature quality. With strong generalization and robustness, least squares support vector machine (LSSVM) is widely applied to nonlinear computations and function approximation. To improve LSSVM model accuracy and efficiency, this paper develops a novel prediction model that uses particle swarm optimization (PSO) combined with grey wolf optimization (GWO) algorithms to optimize the LSSVM model. The generalization performance of the proposed method is validated through comparative experiments using a battery dataset provided by the Center for Advanced Life Cycle Engineering (CALCE) Research Center at the University of Maryland. Experimental results show that the coefficient of determination (R2) consistently exceeds 0.985, with the average absolute error in SOH prediction for four batteries remaining around 0.5%. The comparative experiments demonstrate that the proposed method has a certain degree of accuracy, robustness, and generalization capability.