An improved adaptive Kalman filter algorithm is proposed to tackle a series of issues in estimating the state of charge (SOC) for lithium-ion batteries, including the uncertainty of noise characteristics, sluggish convergence, and poor accuracy in traditional Kalman filter methods. First, an equivalent circuit model of batteries is established, with the model parameters identified and accuracy verified across various temperature and SOC states. Subsequently, positive definiteness optimization is conducted on the calculation method of the covariance matrix for process noise in the traditional adaptive Kalman filter algorithm. In addition, a gain factor is introduced to compensate for the the change of model error in correcting the state estimation results. Finally, the effectiveness of the the proposed algorithm is verified through simulation and testing of experimental batteries. The results indicate that the SOC estimation error is within 4% in different temperature and operating conditions. Compared with the algorithm before improvement and common extended Kalman filter (EKF) algorithm, the improved adaptive Kalman filter algorithm shows better estimation accuracy and convergence speed with relatively strong applicability.