Measurement of topological charges (TC) for vortex beams is a key technology for the practical application of vortex beams. Herein, combining the gradual change of the gradually-changing-period grating with the complete symmetry of the annular grating, a new type of gradually-changing-period annular grating for measuring higher-order TC of vortex beams is developed by optimizing the structure of the ring grating with an additional periodic gradient. Numerical and experimental results demonstrate that a far-field diffraction pattern is formed by collimating the vortex beam onto the ring grating. The results demonstrate that the variation of the patterns accurately corresponds to the orbital angular momentum states of the vortex beams. Consequently, the number of TCs measured in the experiment is ±30. It provides a new measurement method for vortex beams.