We have investigated the electronic structures of a capped single-walled carbon nanotube under the applied electric field using density functional calculations. The capped tube withstands field strengths up to 2 V/Angstrom. When the electric field is applied along the tube axis, charges are transferred from the occupied levels localized at the top pentagon of the cap, and not from the highest occupied level localized at the side pentagon, to the unoccupied levels. We find that the charge densities at the top of the armchair cap show two- or five-lobed patterns depending on the field strength, whereas those of the zigzag cap show a three-lobed pattern. The interpretation for the images of the field emission microscope is also discussed. (C) 2001 American Institute of Physics.