The classical Jiles-Atherton (J-A) equation has been modified through theoretical analysis, which enhances its adaptability under pulsed conditions. Hysteresis loops of Fe-based nanocrystalline cores are measured at different magnetization rates by using an experimental platform for pulsed magnetization properties. The genetic algorithm (GA) is used for J-A parameter identification under pulsed excitation, and the validity of the modified J-A equations is verified by fitting the algorithmically simulated hysteresis loops to the experimentally tested hysteresis loop dataset. Finally, the J-A parameter obtained by GA optimization are applied to the definition of magnetic core parameters in the field-circuit coupling model of the pulse transformer, the simulation and experimental errors when the primary voltage of the pulse transformer is 1.5 kV are analyzed. The results show that the pulse front error of the output waveform is 3.33% and the amplitude error is 2.91%, which is more accurate than the conventional nonlinear solving method of J-A parameter. This indicates that the optimized J-A parameter can be better applied to the modeling and simulation of magnetic-containing components in pulsed power systems.