The accurate prediction of battery dynamics in short and long time scales is essential for advanced battery management and precise systems simulation. A modified-electrochemical impedance spectroscopy-based multi-time-scale fractional-order model is thus proposed to reproduce battery dynamic behaviors both in time and frequency domains. It is first found that the conventional measurement electrochemical impedance spectroscopy (EIS) is pseudo-EIS due to the relatively high open-circuit-voltage variation. The modified EIS is developed to accurately characterize battery internal dynamics in short and long time scales. Noticeably, there is no perfect straight line in the modified EIS at low frequency, and a parallel circuit involving the fractional-order element and resistance is thus adopted to capture battery low-frequency dynamics. Model simulation results show excellent agreement with the experimental data under different dynamic conditions in multi-time-scales, where the maximum relative error is below 0.86%. Model comparison confirms that the proposed model can achieve a higher fidelity. Model validation with three battery chemistries indicates that the proposed modeling methodology showcases good adaptability. Ultimately, the structural composition of the time-domain 1s impedance is theoretically revealed using the proposed model for the first time, allowing to develop the approximate relationship of time-frequency-domain impedances.