The field emission current variation law of carbon nanotube in a large electric field range (0-32 V m-1) is analyzed in depth by combining the density functional theory with metal electron theory. The results show that their emission current densities are determined by their densities of states, the pseudogap, the length and the local electric field, showing the different variation laws in the different electric field ranges. In the lower electric field (corresponding macroscopic field is less than 18 Vm-1), when their density of states increases, their pseudogap decreases: the two trends are opposite, the former increases the number of electrons for emission, and the latter improves the ability to transfer electrons, they all turn to the increase of the emission current, so their field-emission current density increases linearly with increasing electric field in this range. But in the higher electric field (corresponding macroscopic field is less than 32 Vm-1 and more than 18 Vm-1), their densities of states and the pseudogaps take on the same decrease and increase, so do they in the opposite change case, therefore the emission current density behaves as a non-periodic oscillation in the increasing electric field, moreover the higher electric conductivity lead to the rising of current density, the combined effect of the emitter current density exhibits an oscillatory growth in this electric field range, and the carbon nanotubes behave as ionizing radiation. So the too high electric field may cause the emission current to be instable. The electric conductivity variation law of the metallic carbon nanotube is further studied in this paper. In the lower electric field (corresponding macroscopic field is less than 5 Vm-1), the electric conductivity of CNT increases linearly with increasing electric field; when the macroscopic electric field increases up to a value in a range from 5 to 14 Vm-1, the electric conductivity only changes like a slight concussion in (6.3-9.9)1017Sm-1 range, when the macroscopic electric field increases to a value in a range from 16 to 32 Vm-1, the electric conductivity appears as a sharp oscillation growth trend. Additionally, the specific binding energy of CNT is enhanced with increasing electric field, accordingly the structural stability turns better and the cone-capped carbon nanotubes could be used for emission cathode material. The calculation results are consistent with the experimental results of the literature.