This paper proposes a new equivalent circuit model for rechargeable batteries by modifying a double-capacitor model proposed in [1]. It is known that the original model, when compared to other equivalent circuit models, can better address the rate capacity effect and energy recovery effect inherent to batteries. However, it is a purely linear model and includes no representation of a battery's nonlinear phenomena. Hence, this work transforms the original model by introducing a nonlinear-mapping-based voltage source, with the modification justified by an analysis and comparison with the single-particle model. The new nonlinear double-capacitor model is evaluated extensively, with a parameter identification method proposed and validation performed on a number of experimental datasets. The evaluation shows that the proposed model offers excellent predictive capability. With high fidelity and low mathematical complexity, the proposed new model is advantageous for real-time battery management applications.