Lithium-ion batteries have gained significant traction in the energy storage and electric vehicle sectors due to their remarkable attributes such as superior energy density, extended lifespan, and cost-effectiveness. This has made them an appealing choice amidst the energy crisis and the pursuit of carbon peaking and carbon neutrality objectives. Accurate battery simulation methods play important roles in both theoretical research and practical applications of batteries. Currently, most battery simulation methods are based on equivalent circuit models. An impedance spectrum-based simulation method for lithium-ion batteries is presented in this paper. In this method, the fractional-order equivalent circuit model is first developed and the impedance spectrum is used for model parameter identification. Then, the frequency domain model is converted to a time domain model by means of fractional order calculus. Finally, the model is used to perform battery terminal voltage simulations under dynamic working conditions and constant current condition to verify the accuracy of the method.