Abstract: The scattering characteristics by carbon nanotubes in the band of terahertz have been studied. Firstly, the model of scattering by metallic carbon nanotubes has been established. Modal functions give accurate expressions of single-walled carbon nanotubes’ scattered field and transmitted field through rigorous series expansion. Secondly, TM wave is set as an example to study the scattered field and its scattering width properties at normal incidence and oblique incidence by plane wave. The parameters such as scattered field, induced current and scattering width convey the scattering properties efficiently. The results can contribute to terahertz detection technology on a certain extend.