We investigate a novel Smith–Purcell terahertz source. This device is composed of an electron gun, a cylindrical resonator, a metallic grating, and a collector. The characteristics of the Smith–Purcell terahertz source are discussed with the help of three-dimensional particle-in-cell simulation. In this device, coherent and high-power Smith–Purcell radiation (SPR) at the terahertz frequency range can be produced for the reasonable parameters of charge energy and grating. Our results indicate that coherent SPR at 506.529 GHz with a power around 1000 W can be obtained for a grating of period l = 0.3 mm operating at the beam energy E = 50 keV and beamcurrent I = 10 A.