When using the extended Kalman filter (EKF) to estimate the state of charge (SOC) of an electric vehicle power battery, the change of system noise and model parameters may lead to a reduction in estimation accuracy, due to variable operating conditions, battery aging, and other factors. The NCR18650B ternary lithium-ion battery is selected, and the second-order RC model is established with identified parameters. Then, by using EKF as the main body with a fixed measurement noise covariance and adaptively adjusting process noise covariance based on the maximum likelihood estimation criterion, an adaptive extended Kalman filter is built to estimate the SOC of the battery. Simultaneously, a Kalman filter is used to estimate the ohmic resistance in real time. Thus, an adaptive dual extended Kalman filter (ADEKF) algorithm is formed. Finally, algorithm verifications are performed with testing data and public datasets. The ADEKF proposed is used to estimate the SOC of five groups of aged lithium batteries under three operating conditions, which are constant current, dynamic stress test, and Beijing dynamic stress test, and compared with that of EKF and other algorithms. The results show that compared with EKF, the average absolute error of the estimation results of ADEKF for different aged batteries under three operating conditions decreases by 1.868 percentage points, 2.296 percentage points, and 2.534 percentage points, respectively, which proves that ADEKF algorithm can effectively improve the SOC estimation accuracy under multiple operating conditions, battery aging and the combination of the two factors.