Accurate estimation of state of charge is essential to ensure reliable and efficient management of lithium-ion batteries in electric vehicles. The working procedure of lithium-ion batteries is very sophisticated. Thus, developing novel methods for SOC estimation in nonlinear non-Gaussian battery system is inevitable. In this article, a novel adaptive cubature H-infinity filter (ACHF) is proposed. It combines the favorable characteristics of H-infinity (HF) and cubature Kalman filter (CKF). In the iterative process of CKF, the singular value decomposition is used to guarantee non-negative definiteness of the error covariance matrix. The statistical properties of process and measurement noise are timely modified by the Sage–Husa estimator. The performance of the developed method is evaluated by the urban dynamometer driving schedule test. Through the comparison with traditional CKF, the experimental results show that the proposed ACHF method can achieve precise SOC. Moreover, the robustness verification results illustrate that the proposed algorithm is robust to the SOC initial errors.