The generation of optical vortices from nonlinear photonic crystals (NPCs) with spatially modulated second-order nonlinearity offers a promising approach to extend the working wavelength and topological charge of vortex beams for various applications. In this work, the second harmonic (SH) optical vortex beams generated from nonlinear fork gratings under Gaussian beam illumination are numerically investigated. The far-field intensity and phase distributions, as well as the orbital angular momentum (OAM) spectra of the SH beams, are analyzed for different structural topological charges and diffraction orders. Results reveal that higher-order diffraction and larger structural topological charges lead to angular interference patterns and non-uniform intensity distributions, deviating from the standard vortex profile. To optimize the SH vortex quality, the effects of the fundamental wave beam waist, crystal thickness, and grating duty cycle are explored. It is shown that increasing the beam waist can effectively suppress diffraction order interference and improve the beam’s quality. This study provides theoretical guidance for enhancing the performance of nonlinear optical devices based on NPCs.