The instrument decay time constant is an important parameter for a lightning electromagnetic pulse (LEMP) measuring system. So a LEMP sensor with different decay time constants (RC) will demonstrate different frequency response features of the lightning electric field instrument, and the time constant is easily affected by the environment and changes with time. To improve the performance of the lightning electric field instrument, a discrete time-domain model is established through the system identification method. On the basis of the analysis of the calibration method in the time domain and the excitation source selection, the problems of identification modeling within a broadband range of the lightning electric field instrument are discussed. A discrete time-domain model to represent the whole wideband characteristic of an LEMP measurement system can be established by the proposed method. The method can be used to correct the distorted output signal of the lightning electric field instrument. The feasibility of this identified model is verified by laboratory data as well as experimental data of an intracloud flash.