Fourier-transform ghost imaging (FGI) is an imaging method which exploits the high-order correlation characteristics of optical fields to extract the Fourier information of samples. Due to its low requirement for the coherence of the light source, it provides a new technical approach for miniaturizing and high-resolution X-ray microscopy. However, in practice, limited X-ray flux is often required to reduce radiation damage to the sample, and the existence of Compton scattering will reduce the signal-to-noise ratio when X-ray photons interact with the sample. To solve these problems, X-ray FGI with limited flux was studied by simulation. The results showed that when the detection flux was 0.1 PHS/ pixel, the amplitude and phase information of the sample could still be obtained. The Geant4 Monte Carlo simulation program was adopted to analyze the influence of Compton scattering noise generated by the gold, silicon and hemoglobin samples in X-ray FGI. The results indicated that FGI could achieve better Compton scattering noise resistance than traditional X-ray diffraction imaging.