The state of charge (SOC) of lithium‐ion batteries is the main parameter of the battery management system. To improve the accuracy of lithium‐ion battery SOC estimation, this paper uses a double RC physical characteristic circuit network to model the polarization reaction inside the battery and realizes the full parameter identification of the model based on the double‐exponential fitting strategy. Then, using the spherical unscented transform (SUT) to realize the selection of sigma points and the calculation of weight coefficients, at the same time, the adaptive factor is introduced to correct the error covariance matrix in real time and an adaptive spherical unscented Kalman filter (AS‐UKF) algorithm. Finally, the algorithm is compared with the unscented Kalman filter (UKF) and adaptive unscented Kalman filter (AUKF) algorithms through simulation. The results show that the average error of the AS‐UKF algorithm is reduced by 0.5% and 1.18% under the Hybrid Pulse Power Characterization (HPPC) and the Beijing Bus Dynamic Street Test (BBDST) conditions. The AS‐UKF algorithm not only improves the accuracy but also is more stable.