In recent years, the management of lithium-ion power batteries has emerged as a significant area of research in the field of energy storage and electric vehicles. Regarding battery management technology, whether it can accurately establish a battery model that conforms to the actual operating status. The ECM (equivalent circuit model) reflects the dynamic behavior of the battery into a combination of electrical components. All parts of this model have clear physical content and are widely used in the field of battery modeling. In view of the integer-order circuit battery model, this paper introduces fractional-order components to establish a fractional-order ECM, solving the problem that the integer-order model cannot simulate the low-frequency impedance characteristics of the battery well. The parameter identification of the model is the top priority of model establishment. According to the battery current-voltage test data, this paper uses curve fitting and snake optimization algorithm to carry on parameter identification and optimization in the full battery state-of-charge domain. Finally, the established battery fractional-order model is verified using current-voltage data under different working conditions. The results show that fractional-order models provide a better fit to the input-output characteristics of batteries, which meets the needs of practical applications.