The energy distribution of a scanning X-ray probe for XPS, which is equipped with an elliptical mirror monochromator, has been simulated by employing the optical ray tracing method with numerically described Al Kα X-ray and the rocking curve of α-quartz estimated by dynamical diffraction theory. For the evaluation of the validity simulation results, Fermi edge and 3d_5/2 photoelectron spectra of silver were measured by a scanning XPS apparatus. From the simulation results, it was found that the peak energy of diffracted X-ray beam shifted to low energy region when X-ray beam size is increased, however the peak widths of energy distribution curves slightly increased with X-ray beam size. Using the simulated widths and an estimated apparatus function, those results were compared with the experimentally obtained energy widths of silver Fermi edge spectra by Al Ka excitation. The simulation results were in agreement with experimental results. In addition, the relationship between X-ray beam position on the anode and diffracted X-ray energy distribution was also investigated. The shift of peak energy of diffracted X-ray beam was proportional to the distance on the anode from the focal point of elliptical mirror monochromator in energy dispersive direction. Since the simulation results were in good agreement with experimental data, it is concluded that this kind of simulation is effectively used for estimating the beam shape and energy distribution of the diffracted X-ray beam.