The battery’s health status is fundamental to battery health management. Accurately estimating the health status of lithium-ion batteries is crucial for ensuring their safe, reliable, and long-term operation. In this paper, a novel method for estimating the health state of lithium-ion batteries, which is based on grey relational analysis (GRA), Savitzky Golay (SG) filter, and Elman neural network enhanced by sparrow search algorithm (SSA). Firstly, multiple representative health features (HFs) are extracted from the charge and discharge curves. In order to reduce computational complexity, the GRA method is employed for feature analysis and screening, resulting in reasonable, highly relevant, and explanatory HFs. Secondly, to improve the correlation by reducing unstable factors in HF curves, SG filter is utilized for noise reduction and data smoothing, effectively mitigating the influence of data noise and short-term fluctuations resulting from capacity regeneration. Thirdly, in order to accurately estimate the state of health (SOH) of lithium-ion batteries, a SOH estimation model based on SSA-Elman neural network is proposed. The neural network characteristics are optimized to effectively mitigate the issue of Elman network being prone to local optima. Finally, the proposed method’s effectiveness is validated by comparing it with several other methods using NASA dataset. The results show that the RMSE and MAE of the model are controlled within 0.0045 and 0.0038 respectively, and the R2 is maintained above 99.79%, which significantly improves the accuracy and reliability of SOH estimation.