We extend the concept of forked gratings to include the ability of high diffraction orders suppression of a single pair of vortex beams. The main idea is to appropriately distribute rectangular holes over each open space of a conventional forked grating. We further introduce the deep convolutional neural network algorithm to assist us in reconstructing and obtaining the optimal parameter of generalized forked grating. The recovery rate of our neural network is 92.3%. The 3rd order diffracted light intensity can be as low as 0.067% of the desired 1st order diffracted light intensity. The verification experiment results are also presented, confirming the helical phase structures with multitopological charges. The high diffraction orders suppression properties of the generalized forked gratings hold promise for broad applications, such as imaging, microscopy, and fundamental physics observation.