Based on the theory of simple tight-binding, the electronic energy structure of carbon nanotubes has been obtained under the quantitative periodic boundary condition of the carbon nanotubes. Terahertz radiation emitted by carbon nanotubes was demonstrated theoretically by adopting the reported experimental results of the interaction between electron and phonon. The numerical results verify that the carbon nanotubs can generate terahertz radiation and the reason of the terahertz oscillation was analyzed. All results provide a sound theoretical basis for using carbon nanotubes to generate terahertz wave in the experiments.