Based on the Huygens-Fresnel integral and the transmittance function of the fork-shaped grating, analytical expression of a vortex beam passing through a fork-shaped grating is derived. The diffraction characteristics of vortex beams by a fork-shaped grating embedded with topological charge l are studied in great detail. It is shown that the topological charge of the center spot of the diffracted beam is the same as that of the incident vortex beam, and that the topological charge of the nth diffracted beam is nl+m with different diffraction order n. The nth diffracted beam spot is plane wave when it satisfies nl+m=0. While on both sides of the plane wave spot, the doughnut radius of the diffracted beam spot increases as the diffraction order n changes. According to nl+m=0, the topological charge of the incident vortex beam can be detected through the order n of the plane wave spot and the topological charge l embedded in the fork-shaped grating. The results are compared with the experimental results and it is found that they are both in good agreement.