In the ghost imaging, a pseudo-thermal light source is generated by illuminating a diffuser with coherent light. However, in the X-ray region, the incident light of a pseudo-thermal light source is partially coherent, and the spatially partial coherence of the light has a great influence on the imaging quality. The influence of the X-ray partial coherence on the second order correlation function of pseudo-thermal light source is analyzed theoretically using the Gaussian Schell model. The simulation results based on the statistical optics are also given. Both the theoretical and simulated results show that the visibility and resolution of the ghost imaging are influenced by the X-ray spatial coherence. In the case of limited spatial coherence, the visibility of X-ray Fourier-transform ghost imaging can be improved by using a pinhole in front of the diffuser, and the width of the pinhole should be equal to the transverse coherent length of the X-ray. It will be beneficial to achieve the wide applications of X-ray Fourier-transform ghost imaging.