In battery management system (BMS), equivalent-circuit model (ECM) is commonly used to simulate battery dynamics. However, there always is a contradiction between model simplicity and accuracy. A simple model is usually unable to reflect all the dynamic effects of the battery, which may bring errors to parameter identification. A complex model, however, always has too many parameters to be identified and may have parameter divergence problem. This paper tries to solve this problem with a novel ECM by adding a moving average (MA) noise to the one resistor-capacity (RC) circuit model. It can accurately capture the battery dynamics and retain a simple topology. A recursive extended least squares (RELS) algorithm is applied to online identify the ECM parameters, which shows a high accuracy in the experiments. In addition, a battery state-of-power (SOP) prediction algorithm is derived based on the proposed ECM. It considers both the voltage and current limitations of the battery, and offers a two-level prediction of the battery peak power capabilities.