The goal of our paper is to show the design of a Smith–Purcell (SP) terahertz (THz) emitter with two circular and elliptical groove grating structures and its simulations. The SP source is a vacuum-state electronic device that is suitable for generating THz radiation. As a prerequisite for the main goal of the paper, a prebunched electron gun with Gaussian type has been used. Based on the design and simulations, the emitter can radiate THz waves with the frequency of f  =  0.8  THz. Radiation frequency changes by filling grooves of gratings with different glasses. Also, the radiation frequency of emitted waves can be tuned by the types of groove structures and the energy of electrons emitted from electron gun. For simulating the emitter, 3-D particle-in-cell codes and eigenmode solver have been utilized.