State of charge (SOC) is the key to measuring the safety of batteries. SOC value represents the residual capacity of batteries, which cannot be directly determined by measuring instruments but needs to be calculated by parameters such as voltage, current, and temperature. However, there is nonlinear relationship between these measurable data and SOC. In this paper, the second-order equivalent circuit model is used as the battery operating characteristic description model, the Sage-Husa adaptive algorithm and square root filter is introduced based on the Unscented Kalman Filter (UKF) algorithm, namely a Square Root Adaptive Unscented Kalman Filter (SRAUKF) algorithm is proposed. The SRAUKF replaces the state error covariance matrix with the square root of the state error covariance matrix. The SRAUKF algorithm is formed to improve the precision of SOC estimation. In this paper, the UKF algorithm and the SRAUKF algorithm are respectively used to estimate the SOC value of lithium batteries. The SOC estimation and absolute error curves of the two algorithms are compared and analyzed under the given initial value and different noise variance. Experiments reveal that the SRAUKF algorithm displays better noise suppression ability, higher response speed, and greater estimation accuracy than the UKF algorithm.