The estimation of state of health (SOH) of a lithium-ion battery (LIB) is of great significance to system safety and economic development. This paper proposes a SOH estimation method based on the SSA-Elman model for the first time. To improve the correlation rates between features and battery capacity, a method combining median absolute deviation filtering and Savitzky–Golay filtering is proposed to process the data. Based on the aging characteristics of the LIB, five features with correlation rates above 0.99 after data processing are then proposed. Addressing the defects of the Elman model, the sparrow search algorithm (SSA) is used to optimize the network parameters. In addition, a data incremental update mechanism is added to improve the generalization of the SSA-Elman model. Finally, the performance of the proposed model is verified based on NASA dataset, and the outputs of the Elman, LSTM and SSA-Elman models are compared. The results show that the proposed method can accurately estimate the SOH, with the root mean square error (RMSE) being as low as 0.0024 and the mean absolute percentage error (MAPE) being as low as 0.25%. In addition, RMSE does not exceed 0.0224 and MAPE does not exceed 2.21% in high temperature and low temperature verifications.