With the rapid development of battery-powered electric vehicles, the lithium-ion battery plays a critical role in the reliability of vehicle system. In order to provide timely management and protection for battery systems, it is necessary to develop a reliable battery model and accurate battery parameters estimation to describe battery dynamic behaviors. Therefore, this paper focuses on an on-board adaptive model for state-of-charge (SOC) estimation of lithium-ion batteries. Firstly, a first-order equivalent circuit battery model is employed to describe battery dynamic characteristics. Then, the recursive least square algorithm and the off-line identification method are used to provide good initial values of model parameters to ensure filter stability and reduce the convergence time. Thirdly, an extended-Kalman-filter (EKF) is applied to on-line estimate battery SOC and model parameters. Considering that the EKF is essentially a first-order Taylor approximation of battery model, which contains inevitable model errors, thus, a proportional integral-based error adjustment technique is employed to improve the performance of EKF method and correct model parameters. Finally, the experimental results on lithium-ion batteries indicate that the proposed EKF with proportional integral-based error adjustment method can provide robust and accurate battery model and on-line parameter estimation. (C) 2017 Elsevier B.V. All rights reserved.