Due to the digital control delay and difference of sampling point position, the average model cannot accurately describe the nonlinear characteristics and frequency response of digital controlled Boost converters with Leading Edge Modulation (LEM) and Trailing Edge Modulation (TEM), while the sampled-data modeling method can accurately predict due to the lack of simplified high-frequency information analysis. However, the sampled-data model has no intuitive physical meaning. In this paper, the improved approximation method of discrete iterative method is used to model the digitally controlled Boost converter. By sampling the state variables with discrete time, both large-signal models of the Boost converter with LEM and TEM were derived, and the second-order global equivalent circuits were obtained. Based on the proposed large-signal model, the z-domain small-signal model of Boost converter can be derived, and the frequency response of the system under different modulation modes can be analyzed and compared. Finally, the accuracy of the model and theoretical analysis are verified through experiment.