The electro-optical modulation effect of a (10,0) boron nitride nanotube is investigated by first-principles, density functional theory calculations. The optical properties of boron nitride nanotubes can be tuned through perturbation by a transverse electric field. Large optical anisotropy in variations of the absorption spectra and refractive indices in response to external electric field is found. In addition, a method called the band-resolved absorption density analysis technique is developed to investigate the detailed optical absorption transition processes. The result is consistent with the recent experimental observation [ M. Ishigami et al., Phys. Rev. Lett. 94, 56804 (2005) ] and suggests that the boron nitride nanotubes can be a promising material for electro-optical modulation device applications.