Lithium-ion batteries are widely used in many fields, and accurate prediction of their remaining useful life (RUL) was crucial for effective battery management and safety assurance. In order to solve the problem of reduced RUL prediction accuracy caused by the local capacity regeneration phenomenon during battery capacity degradation, this paper proposed a novel RUL prediction method, which combined complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) technique with an innovative hybrid prediction strategy that integrated the support vector regression (SVR) and the long short-term memory (LSTM) networks. First, CEEMDAN was used to decompose the battery capacity data into high-frequency and low-frequency components, thereby reducing the impact of capacity regeneration. Subsequently, the SVR model predicted the low-frequency component that characterized the main degradation trend, and the high-frequency component that contained capacity regeneration features was predicted using an LSTM network optimized by the sparrow search algorithm (SSA). Finally, the final RUL prediction was obtained by combining the predictions of the two models. Experimental results on NASA public datasets showed that the proposed hybrid method significantly outperformed existing methods: the RMSE of the methods proposed in this paper were all less than 0.0086 Ah, the MAE were all less than 0.0060 Ah, the R