To suppress the high-order diffraction of traditional fork gratings, a single optical element, the fork modulated groove position grating (FMGPG), is proposed, which can effectively suppress undesired high-order diffraction by adjusting the center position of grating lines. Numerical simulations and experimental results indicate that the FMGPG has a good single-order diffraction characteristic and can effectively suppress undesired high-order diffraction, which is almost consistent with the theoretical prediction. The third-order diffraction light intensity can be reduced from 24% of the required first-order diffraction light intensity to a degree less than the light intensity of the background. The suppression effects of periods, maximum movement distance, and graph areas on high-order diffraction are analyzed. Meanwhile, it is confirmed that the output beams have helical phase structures with multiple topological charges. The high-order diffraction suppression characteristic of the proposed gratings has broad application prospects in aspects such as imaging, microscopy, and particle capture.