The compact terahertz (THz) radiation source based on Smith-Purcell (SP) effect has been expected to be the next-generation table-top THz free electron laser (THz-FEL). We have performed a numerical simulation of the generation of SP radiation at THz frequency under the condition of using the electron beam (e-beam) with high repetition THz frequency by simplified particle-in-cell finite difference-time domain (PIC-FDTD) method, and clarified that frequency of SP radiation can be tuned with pre-bunch frequency of e-beam. Our results can lead to the development of more tunable table-top THz-SP-FEL.