In this paper, an estimation algorithm for state of charge (SOC) was applied using an equivalent circuit model (ECM) and an Extended Kalman Filter (EKF) to improve the estimation accuracy of the battery system states. In particular, an observer was designed to estimate SOC along with the aged capacity. In the case of the fresh battery, when SOC was estimated by Kalman Filter (KF), the mean absolute percentage error (MAPE) was 0.27% which was smaller than MAPE of 1.43% when the SOC was calculated by the model without the observer. In the driving mode of the vehicle, the general KF or EKF algorithm cannot be used to estimate both SOC and capacity. Considering that the battery aging does not occur in a short period of time, a strategy of periodically estimating the battery capacity during charging was proposed. In the charging mode, since the current is fixed at some intervals, a strategy for estimating the capacity along with the SOC in this situation was suggested. When the current was fixed, MAPE of SOC estimation was 0.54%, and the MAPE of capacity estimation was 2.24%. Since the current is fixed when charging, it is feasible to estimate the battery capacity and SOC simultaneously using the general EKF. This method can be used to periodically perform battery capacity correction when charging the battery. When driving, the SOC can be estimated using EKF with the corrected capacity.