Measuring orbital angular momentum (OAM) states of vortex beams is of great importance in diverse applications employing OAM-carrying vortex beams. We present a simple and efficient scheme to measure OAM states (i.e. topological charge values) of vortex beams with annular gratings. The magnitude of the topological charge value is determined by the number of dark fringes after diffraction, and the sign of the topological charge value is distinguished by the orientation of the diffraction pattern. We first theoretically study the diffraction patterns using both annular amplitude and phase gratings. The annular phase grating shows almost 10-dB better diffraction efficiency compared to the annular amplitude grating. We then experimentally demonstrate the OAM states measurement of vortex beams using annular phase grating. The scheme works well even for high-order vortex beams with topological charge value as high as ± 25. We also experimentally show the evolution of diffraction patterns when slightly changing the fractional topological charge value of vortex beam from 0.1 to 1.0. In addition, the proposed scheme shows potential large tolerance of beam alignment during the OAM states measurement of vortex beams.