Compared with traditional phase-contrast imaging methods, the X-ray single grating phase-contrast imaging based on Fourier transform has the advantages of low radiation dose and fast imaging speed, and has a broad application prospect in the fields of materials and medical treatment. The extraction of object spectral information is a key step to recover the phase using this technique, but the extraction process is easily affected by Moiré artifacts, which leads to the degradation of the imaging quality and in turn limits the development and application of this method. In view of the above problems, based on the theoretical analysis of Moiré artifacts and the structural characteristics of the imaging system, two schemes by rotating grating and adjusting the projection frequency of grating are proposed to eliminate the artifacts, and their feasibilities are verified successfully in experiments, providing a reference for the promotion and application of X-ray single grating phase-contrast imaging.