State-of-charge is an important indicator for guiding the charging-discharging operation of lithium-ion batteries. In this paper, an improved adaptive battery state estimator is proposed, which estimates the state-of-charge accurately under both the constant current constant voltage charging conditions and various dynamic operating conditions. Besides, the state-of-charge estimation error is less than 3% under various common perturbations and parameter uncertainties, including the uncertainty of battery capacity, the Gaussian white noise and the biases of the sensors, which proves the robustness of the estimator. Generally, the drivers prefer to charge the electric vehicles after every driving. In other words, the lithium-ion batteries are likely to be charged or discharged from any state-of-charge and polarization state. In order to simulate this usage habit, several data segments are picked out from original data for state-of-charge estimation. Experiment results show that the state-of-charge estimation error reaches and remains within 3% rapidly under both the constant current constant voltage charging conditions and the dynamic discharging conditions. In conclusion, the improved adaptive battery state estimator is a promising algorithm for engineering application.