Terahertz wave is an important band for 6G communication in the future and has become a hot issue studied in the optics and electronics fields. However, the terahertz source, especially the integrated terahertz source based on micro-nano optics, gets a lot of attention. In this paper, a broadband terahertz radiation source is proposed, and it is based on the plasmonic resonant characteristics of the nano-antenna array. Using Maxwell's equation and a hydrodynamic equation of the metal plasma, this paper studies the terahertz time-domain wave generation from the nano-antenna array excited by a pulsed laser. The results show that the polarization of the generated terahertz radiation is perpendicular to the polarization of the incident light, and the terahertz emission bandwidth is closely related to the pulse width of the exciting laser. A nano-antenna array is designable and easy to integrate, and thus it is expected to be better applied in integrated terahertz source devices. This paper will provide a theoretical basis for the design of terahertz source based on surface plasmonics in the future.