The electronic structures of boron nitride nanotubes (BNNTs) doped by different organic molecules under a transverse electric field were investigated via first-principles calculations. The external field reduces the energy gap of BNNT, thus makes the molecular bands closer to the BNNT band edges and enhances the charge transfers between BNNT and molecules. The effects of the electric field direction on the band structure are negligible. The electric field shielding effect of BNNT to the inside organic molecules is discussed. Organic molecule doping strongly modifies the optical property of BNNT, and the absorption edge is red-shifted under static transverse electric field.