Using the tight-binding approach with the WKB method，we study the Peierls phase transition of the single-wall carbon nanotube and the field emission in a magnetic field along the tube axis. We find that the Peierls phase transition may occur above room temperature，which induces an energy gap near the Fermi level，leading to the metal-semiconducting phase transition of the carbon nanotubes. The Peierls distortion of the carbon nanotubes suppresses the field emission current. The Peierls distortion may be modified by the magnetic field applied along the tube axis. The energy band structure of the carbon nanotubes depends on the competition between the Peierls distortion and the magnetic field effect，which affects the field emission current of the carbon nanotubes.