X-ray grazing incidence microscopy has extensive applications in the fields of laser inertial confinement fusion and synchrotron radiation. Monte Carlo methods can be used to determine the optical performance of X-ray grazing incidence microscopes and predict the experimental results, which is of great significance for studying physical experiments and diagnostics. In this paper, we proposed a Monte Carlo method based on Geant4 for studying X-ray grazing incidence microscopy. We introduced the G4MultilayerReflection class to describe the physical processes of X-ray multilayer mirrors. We designed a dual-energy Kirkpatrick-Baez microscope that can operate at 6.4 and 9.67 keV simultaneously. Monte Carlo simulations of the spatial resolution and throughput efficiency of the microscope were performed using Geant4, which was assembled and characterized. The spatial resolution results obtained by the Geant4 laboratory simulations, the theoretical model, and the experiments were in good agreement. Additionally, we conducted throughput efficiency calibration experiments for the 6.4 keV imaging channel. The difference between the experimental and Geant4-simulated throughput efficiency was evaluated and resulted in root mean square error values of 8.7% and 9.5% along the Y- and Z-axes, respectively.