A battery’s state-of-charge (SOC) can be used to estimate the mileage an electric vehicle (EV) can travel. It is desirable to make such an estimation not only accurate, but also economical in computation, so that the battery management system (BMS) can be cost-effective in its implementation. Existing computationally-efficient SOC estimation algorithms, such as the Luenberger observer, suffer from low accuracy and require tuning of the feedback gain by trial-and-error. In this study, an algorithm named lazy-extended Kalman filter (LEKF) is proposed, to allow the Luenberger observer to learn periodically from the extended Kalman filter (EKF) and solve the problems, while maintaining computational efficiency. We demonstrated the effectiveness and high performance of LEKF by both numerical simulation and experiments under different load conditions. The results show that LEKF can have 50% less computational complexity than the conventional EKF and a near-optimal estimation error of less than 2%.