To improve the accuracy of remaining useful life (RUL) prediction for lithium-ion batteries, a method combining complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), random forest (RF), improved hazelnut tree search (IHTS) algorithm and improved gated recurrent unit (GRU) is proposed. First, CEEMDAN is used for modal decomposition and noise reduction on the original capacity data. Second, RF is adopted to calculate the weight of each modal component relative to the original capacity data. Third, chaos initialization optimization is employed to improve a hazelnut tree search algorithm to obtain the IHTS algorithm, which is further used to optimize and improve GRU to establish an IHTS-GRU model. Finally, the IHTS-GRU prediction results of each modal component and the weight of each modal component are weighted and averaged, thus realizing the lithium-ion battery RUL prediction. The NASA data is used for verification, and it is found that the prediction accuracy of the CEEMDAN-RF-IHTS-GRU model is improved by 3.2% and 2.1% on average compared with those of the CEEMDAN-GRU and CEEMDAN-RF-GRU models, respectively, indicating significant increases in the prediction accuracy. Therefore, the proposed method improves the accuracy of RUL prediction for lithium-ion batteries.