A novel scheme for generating relativistic high-order harmonics by a relativistic radially polarized laser interacting with a plasma annular grating is proposed. The particle-in-cell results show that the radial laser field can drive the relativistic electron bunches to oscillate radially in all azimuth directions, resulting in the emission of strong harmonics. Firstly, the interference of the laser field on the plasma grating structure significantly enhances the radiated harmonics which match the phase conditions. Secondly, due to the common ring symmetry of the grating structure and laser polarization, the transverse distribution of harmonics presents a Bessel form, and there is a sharp bright spot in the center with relativistic intensity. Such high-intensity short-wave structured harmonics have broad applications in areas such as plasma diagnostics, high resolution imaging and detection.