In order to solve the problem that the traditional Thevenin equivalent circuit models’ parameters of lithium-ion batteries cannot be identified under the constant current, constant voltage and / or constant power charge / discharge, a new equivalent timevarying internal resistance model is proposed. The analyses show that, when the open circuit voltage and internal resistance of a lithium-ion battery are characterized as an unknown time-varying voltage and internal resistance, respectively, the amp-hour integral and random walk model can be used to describe the evolutions of unknown time-varying voltage and internal resistance. Accordingly, an equivalent time-varying internal resistance model with a state space formula can be used to illustrate the characteristics of lithiumion battery. It is also shown that the transient polarization voltage produced by the battery charge and discharge can be explained by combining the product of end current at the battery and the time-varying internal resistance with the observed noise. Compared with the traditional model, the root-mean-square error of SoC estimation is reduced by 48% on average under constant current, voltage and power conditions. The correctness and effectiveness of our model and analytical results are verified by both the dataset based on the internet and experimental results.