As one crucial function of a battery management system (BMS), the state of health (SOH) prediction of a lithium-ion battery is of great significance to safe system operation and the battery’s service life. This paper proposes a framework for SOH prediction, which includes the feature points extraction and SOH prediction. First, based on the incremental capacity (IC) curve, the improved incremental capacity (IIC) curve is deduced by taking the derivative of the IC curve, and the grey relational analysis (GRA) is adopted to select the four feature points with the highest grey relational grade (GRG). Then, an improved sparrow search algorithm (ISSA) is proposed to optimize the parameters of the support vector regression (SVR) for more precise SOH prediction. Finally, experiments are carried out and the results show that the proposed feature points extraction method based on the IC/IIC curves and GRA is efficiently to improve the SOH prediction accuracy. Furthermore, compared with three traditional algorithms, the ISSA-SVR can restrict the SOH prediction error within 1.7%, and it also shows the proposed SOH prediction framework has strong robustness and high universality.