Ab initio calculations demonstrated that the energy gap modulation of a chiral carbon nanotube with mono-vacancy defect can be achieved by applying a transverse electric field. The bandstructure of this defective carbon nanotube varying due to the external electric field is distinctly different from those of the perfect nanotube and defective zigzag nanotube. This variation in bandstructure strongly depends on not only the chirality of the nanotube and also the applied direction of the transverse electric field. A mechanism is proposed to explain the response of the local energy gap between the valence band maximum state and the local gap state under external electric field. Several potential applications of these phenomena are discussed.