The accelerator-based syringe needle-type proton-induced X-ray source, which was proposed by the authors in 2013 as an alternative for prostate cancer brachytherapy, has an essential issue in that its dose distribution is affected by many factors, such as the structure of the needle and incident proton beam conditions. In this paper, as a method of evaluating dose distribution, we propose a Geant4 simulation to study the effect of the incident proton beam condition on the spectrum and distribution of X-ray emission, using experimentally measured proton beam emittance as input data. The results showed that the effect of beam misalignment was significant and confirmed the effectiveness of this method. It is expected that improving this method will clarify the other factors that affect X-ray distribution, so that finally, we can optimize such factors in designing a special dose distribution for the irradiation of tumors of arbitrary size and shape in the tissue.