We present first-principles calculations of quantum transport which show that the resistance of metallic carbon nanotubes can be changed dramatically with homogeneous transverse electric fields if the nanotubes have impurities or defects. The change of the resistance is predicted to range over more than 2 orders of magnitude with experimentally attainable electric fields. This novel property has its origin that backscattering of conduction electrons by impurities or defects in the nanotubes is strongly dependent on the strength and/or direction of the applied electric fields. We expect this property to open a path to new device applications of metallic carbon nanotubes.