A beam-scanning terahertz (THz) radiation mechanism in a free-electron-driven grating system is proposed for THz applications. By loading a period-asynchronous rod array above the grating, the spoof surface plasmon (SSP) originally excited by the electron changes its radiation characteristics owing to the rod-induced Brillouin zone folding effect. The rod array functions as an antenna and converts the SSP into a spatial coherent THz radiation. The radiation frequency and direction can be precisely controlled by the electron energy. The field intensity of the radiation is increased approximately 20 times compared with that of the conventional Smith-Purcell radiation in the same frequency range. In addition, a microwave-band scaling prototype is fabricated and the frequency-controlled radiation is measured. Excellent agreement between the experimental and simulated results is obtained. This study paves the way for the development of on-chip THz sources for advanced communication and detection applications.