When using the extended Kalman filter (EKF) to estimate the state of charge (SOC) of lithium-ion batteries (LIBs), the noise covariance matrices of system and observation noises for energy harvesters are mostly given randomly, which makes it impossible to optimize the noise problem. This results in the low accuracy and stability of SOC estimation. To address these problems, a method of estimating the SOC of power LIBs based on long short-term memory–adaptive unscented Kalman filter (LSTM–AUKF) fusion is proposed to improve the accuracy and stability of estimating the SOC of LIBs. First, the offline parameters of the Thevenin model are identified from the hybrid pulse power characterization (HPPC) experimental data. Then, the LSTM structure of the SOC estimation window is constructed for power LIBs, and the power battery SOC training network is predicted in real time from the power battery current, voltage, temperature, and historical data. Finally, the AUKF algorithm for estimating the SOC of power LIBs is designed, then a fusion strategy is proposed. The experimental validation shows that the root mean squared error (RMSE), maximum (MAX), and mean absolute error (MAE), used to estimate the SOC of the LSTM–AUKF hybrid power lithium battery in the research window, are 1.13, 1.74, and 0.39%, respectively. Compared with the window LSTM network, the fusion algorithm improves the accuracy and stability of SOC estimation for power LIBs.