Dynamic modeling and state of charge (SOC) estimation of lithium-ion batteries (LIBs) is a critical technology in the battery management system. Aiming at the essential nonlinear characteristics of LIBs and the time-varying operating state caused by the influence of the external environment including load changes and other factors, this paper proposes to adopt the state-dependent autoregressive model with exogenous inputs (SD-ARX) to describe its nonlinear dynamic characteristics. This type of model first constructs state signal quantities that can characterize the dynamic properties of LIBs and uses them as inputs to the radial basis function neural network to approximate the functional-type coefficients of the SD-ARX model, which is used to guide the model to represent the nonlinear dynamic properties of LIBs under different operating states. Benefiting from the model can be represented as a linear combination of nonlinear functions, the model parameters identified offline by a structured nonlinear parameter optimization method. Finally, the SOC is estimated online using an adaptive extended Kalman filter based on the established model. The results show that the method can reliably estimate the SOC of a battery under different working conditions and a relatively wide temperature range and achieves a balance between accuracy and real-time performance.