Accurate prediction of the state of health (SOH) and remaining useful life (RUL) of lithium-ion batteries is of great significance for their safe and stable operation. In this paper, a novel Algorithm combining the improved hippopotamus optimization algorithm (IHOA) and deep extreme learning machine (DELM) is proposed. Six health indicators (HIs) were extracted from the charge and discharge process of lithium batteries, and the five HIs with high capacity correlation were retained by Pearson correlation analysis. Then, the outliers in the feature data were removed and normalized by Hampel filtering. Finally, the DELM model of SOH and RUL is established. In addition, In order to improve the prediction efficiency of the model, an IHOA is proposed to optimize the hyperparameters of DELM. Compared with the traditional hippopotamus optimization algorithm (HOA), it solves the limitations of the traditional hippopotamus algorithm in search efficiency, convergence speed and global search. The experimental simulation results based on CALCE lithium battery data set show that the prediction accuracy of IHOA-DELM algorithm is high, the root mean square error (RMSE) of SOH prediction of the proposed method ranges from 1.21%~1.31%, and the mean absolute error (MAE) value ranges from 0.89%~0.95%. The mean absolute percentage error (MAPE) was between 1.59%~1.93%. The maximum absolute error (AE) value predicted by RUL does not exceed 3 cycles, and the minimum absolute error value is only 1 cycle.