To generate high-order and fractional-order vortex beams， a spatial light modulator was used to simulate a forked grating. This was performed to generate and isolate the desired vortex beams with the different orbital angular momentum (OAM) of l, and investigated their characteristics. Measurement of their topological charges via the interference method validated the availability and the accuracy of the experimental method. An optical path for vortex beam generation was designed， and a computer program was developed to create a forked grating hologram. This grating was simulated using a transmissive spatial light modulator and uploaded on the modulator as a hologram. By adjusting the parameters， the holographic grating pattern could be modified to produce integer-order vortex beams with topological charges ranging from 1.00 to 100.0. In addition， fractional-order vortex beams were generated at intervals of 0.1. The first order diffraction was isolated using an aperture diaphragm. Subsequently， its characteristics were analyzed， and its topological charge was measured via interferometry. A consistent relationship was observed between the distributions of integer- and fractional-order light fields and their respective topological charge numbers. Notably， as the topological charge number neared 100， a marked reduction was observed in the beam quality. The topological charge number， determined via interferometry， matched the parameters set in the computer-generated hologram， validating the computer-generated holography method's accuracy. Given its straightforward setup and adjustable parameters， this method could serve as a reference for the creation and application of high-order and fractional-order vortex light.