The accurate prediction of lithium-ion battery state of health (SOH) can extend battery life, enhance device safety, and ensure sustained reliability in critical applications. Addressing the non-linear and non-stationary characteristics of battery capacity sequences, a novel method for predicting lithium battery SOH is proposed using a deep hybrid kernel extreme learning machine (DHKELM) optimized by the improved black-winged kite algorithm (IBKA). First, to address the limitations of traditional extreme learning machines (ELMs) in capturing non-linear features and their poor generalization ability, the concepts of auto encoders (AEs) and hybrid kernel functions are introduced to enhance ELM, resulting in the establishment of the DHKELM model for SOH prediction. Next, to tackle the challenge of parameter selection for DHKELM, an optimal point set strategy, the Gompertz growth model, and a Levy flight strategy are employed to optimize the parameters of DHKELM using IBKA before model training. Finally, the performance of IBKA-DHKELM is validated using two distinct datasets from NASA and CALCE, comparing it against ELM, DHKELM, and BKA-DHKELM. The results show that IBKA-DHKELM achieves the smallest error, with an RMSE of only 0.0062, demonstrating exceptional non-linear fitting capability, high predictive accuracy, and good robustness.