Accurate estimation of the state of charge （SOC） is crucial for prolonging battery life and reducing the occurrence of accidents. Aiming at the problems of modeling errors in lithium battery systems and the poor adaptability of traditional methods in a wide temperature range，an adaptive gain sliding mode observer （AGSMO） was designed to improve the accuracy of SOC estimation. A second-order RC equivalent circuit model was used to construct the state equation which was applicable to AGSMO，and combining the forgetting factor recursive least square （FFRLS） algorithm to complete the identification of the model parameter. The equivalent control idea was used to construct the equivalent expression of the state error. Based on this，a sliding mode observer was designed，and a new adaptive gain was adopted to increase the convergence speed and suppress chattering. Combined with the case simulation，the results show that the AGSMO can achieve accurate SOC estimates under different initial value conditions in both United States federal urban driving schedule FUDS and highway driving schedule US06 tests，and the above two tests verify that AGSMO has better estimation accuracy and convergence speed than sliding mode observer （SMO） and extended Kalman filter （EKF） in a wide temperature range，the root mean square error is not more than 0.68%，and shows strong robustness at both ends of the temperature range.