Extensive research has been conducted on generating THz waves using Smith-Purcell radiation, yet a portion of the electron bunch's interaction energy with the gratings is confined to the metal gratings' surface, leading to a low THz radiation power. This paper experimentally demonstrates that metal gratings with a dielectric substrate can emit the resonant modes in surface waves when excited by relativistic femtosecond electron bunches. The observed spectra of the resonant THz waves align well with the theoretical estimations derived from the configuration's dispersion relation and 3D simulations. In comparison to traditional Smith-Purcell radiation generated by the grating, these resonant THz waves exhibit significantly higher intensity and improved orientation. Additionally, we investigated the radiation characteristics of the resonant THz waves, including radiation angle, beam-grating distance, beam energy, and bunch length. This innovative approach presents a novel method for generating high-power coherent terahertz radiation.