Tabletop nanoscale microscopy can be performed using X-ray Fourier-transform ghost imaging (FGI). However, the X-ray source used in a tabletop FGI system is one miniaturized laboratory source with poor monochromatic quality, making it difficult to directly obtain high-quality diffraction patterns from a sample. To obtain high-quality patterns, the theoretical derivations and numerical simulations on FGI using a polychromatic source were performed. The mechanism of the influence of polychromatic light on the distortion of diffraction patterns in FGI was clarified, and further a diffraction-pattern correction method was proposed. Based on the scaling relation between the different X-ray wavelengths and the corresponding diffraction patterns, a matrix equation was derived linking the diffraction pattern of a sample and the polychromatic-intensity correlation function, using which the diffraction pattern of the sample can be obtained.