A theoretical formalism is developed to study the intrinsic properties of field emission from the single-walled carbon nanotubes (SWCNTs), including the current-voltage characteristic, the energy spectrum, and their responses to the magnetic field. The SWCNTs can be classified to two kinds, metallic and semiconducting tubes, according to field-emission properties. They have different slopes of the Fowler-Nordheim [Proc. R. Soc. London, Ser. A 119, 173 (1928)] plot, energy spectra, and different responses to the magnetic field, which originate from the energy band structure of SWCNTs. (c) 2006 American Vacuum Society.