In order to improve the state of charge (SOC) estimation accuracy of lead-acid battery under random conditions, reduce the influence of error variation on estimation accuracy. Aiming at the limitation of fixed length selection of error innovation sequence in adaptive extended Kalman filter, an improved adaptive extended Kalman filter algorithm is proposed to estimate SOC. The likelihood estimation is used to monitor the distribution change time of the error innovation sequence in the covariance matching algorithm, and the length of the innovation sequence is adaptively adjusted according to the distribution change of the error innovation, thereby reducing the error when estimating SOC. Firstly, the equivalent model parameters are identified by the recursive least squares method with forgetting factor ( FFRLS ), the average error voltage of the model is 13. 63 mV. Then, in the random condition experiment, it is found that the improved algorithm improves the accuracy of RMSE and MAE performance by 14. 44% and 17. 26% respectively when estimating SOC. The results show that the improved algorithm has better stability and accuracy.