Perfect optical vortices (POVs) are beams whose topological charges are independent of radius, unlike conventional optical vortices. POVs are the Fourier transformation of Bessel-Gaussian (BG) beams and can be seen in the far-field diffraction of BG beams. In this paper, we present the generation of POVs of arbitrary charge using curved fork grating (CFG) illuminated by BG beam. For this purpose, first, a theoretical study of the Fresnel-Kirchhoff integral for diffraction of a BG beam by CFG is completed. The analytical results show the presence of vortex beams with various topological charges in diffraction orders. Then, diffraction of the BG beam with the order (l) by CFG with a topological charge (p) is numerically simulated. Additionally, experimental results prove the generation of POVs in diffraction orders. Also, experimental interference patterns obtained by interfering a POV and Gaussian beam confirm the ability of analytical solutions to determine the topological charges of vortex beams. Comparison of the results reveals the validity of the analytical, simulation, and experimental results.