The lithium-ion battery is the power source of an electric vehicle, so it is of great significance to estimate the state of charge (SOC) of lithium-ion batteries accurately to ensure vehicle safety. To improve the accuracy of the parameters of the equivalent circuit model for batteries, a second-order RC model for ternary Li-ion batteries is established, and the model parameters are identified online based on the forgetting factor recursive least squares (FFRLS) estimator. To improve the accuracy of SOC estimation, a novel fusion method, IGA-BP-AEKF, is proposed. Firstly, an adaptive extended Kalman filter (AEKF) is used to predict the SOC. Then, an optimization method for BP neural networks (BPNNs) based on an improved genetic algorithm (IGA) is proposed, in which pertinent parameters affecting AEKF estimation are utilized for BPNN training. Furthermore, a method with evaluation error compensation for AEKF based on such a trained BPNN is proposed to enhance SOC evaluation precision. The excellent accuracy and stability of the suggested method are confirmed by the experimental data under FUDS working conditions, which indicates that the proposed IGA-BP-EKF algorithm is superior, with the highest error of 0.0119, MAE of 0.0083, and RMSE of 0.0088.