Equivalent circuit model (ECM) can reflect the internal working process of lithium-ion batteries (LIBs) and estimate the critical state of LIBs. However, conventional ECMs struggle to accurately describe the operation of LIBs at a low state of charge (SOC), and their adaptability under various operating conditions is limited. In this article, we propose a nonlinear equivalent circuit model that is based on electrochemical impedance spectroscopy (EIS) and takes into account the solid-phase diffusion process, which improves the model performance in low SOC conditions. First, this article establishes an ECM based on the shape of the electrochemical impedance spectrum. Then, by introducing a solid-phase diffusion process, the performance of the ECM in low SOC conditions is enhanced. Finally, the results demonstrate that the proposed model exhibits higher accuracy than traditional ECMs under various operating conditions.