A novel nano-antenna for the generation and applications of terahertz wave and the Pocklingtons integral equation are proposed based on the carbon nanotube structure. The radiation characteristics of carbon nanotube antenna in terahertz range have been investigated by numerical simulation and theoretical computation. Both the numerical and analytical results demonstrate that the antenna with half wave length of 60μm takes on the dual frequency properties at the center frequencies of 2.5THz and 7.6THz，with the corresponding -10dB return loss (S11) bandwidths of 8.4% and 2.7%，respectively. Compared with the gain of 0.598dB of a single dipole antenna the maximum gain of a typical 10×10 carbon nanotube antenna array is 10.30dB. The results could be useful for the design of carbon nanotube antenna arrays for generating terahertz wave.