The state of charge (SOC) is a critical parameter of a Li-ion battery, which is the most important energy storage in Electric Vehicles (EVs) and the Smart Grid. An accurate on-line estimation of the SOC is important for forecasting the EV driving range and battery energy storage system (BESS) power dispatching. A good estimation of the SOC results from a good identification of the battery parameters. Reducing the algorithm complexity is important to improve the accuracy of SOC estimation results. Several methods of identification are used, among them; we use the adaptive neurons networks, ADALINE. The advantage of this approach is the speed of execution (fast training) as well as the possibility of interpreting these weights. In this paper, after considering a resistor-capacitor (2RC) circuit-equivalent model for the battery, a parameter identification technique is applied to the real current and voltage data to estimate and update the parameters of the battery at each step. Subsequently, a reduced-order linear observer is designed for this continuously updating model to estimate the SOC as one of the states of the battery system. In designing the observer, a mixture of Coulomb counting and VOC algorithm is combined with the adaptive parameter-updating approach based on the ADALINE.