On the basis of the tight-binding theory，we derived the band structure formula of carbon nanotube field-effect transistors with/without a magnetic field. The results show that the band gap becomes zero periodically with increasing strength of the magnetic field，which indicates that the magnetic field can change the nature of the conductivity of carbon between the metal-type and semiconductor-type with 0.50 for the period. Furthermore，by using Natori theory on the field-effect transistor, we studied the influence of applied magnetic field on the current-voltage characteristics of carbon nanotube field-effect transistors. The results show that in the two types of zigzag and armchair carbon tubes the conductivity oscillates with the voltage and the magnetic field and the oscillation behaviors are obviously different for these two types of carbon nanotubes.