Boron nitride nanoribbon (BNNR) is a one-dimensional single layer nano-material with finite width and infinite length. Bent BNNR will show some unique electronic properties because of the rotation of Pz orbit. The software DMOL3 of Material Studio, based on the first principles, can be used to calculate the energy band, and the band gap will change with the bending angle; in the armchair BN nanoribbons the change is more obvious. Band gaps of zigzag BN nanoribbons may change more than those in armchair BN nanoribbons do if the external electric field is also added on the bent BN nanoribbons. When the electric field is increased to a certain value, nanoribbons will transit from semiconductor to metal, and it is important that the corresponding critical electric field value depends on the bending angle. The modulation of electric field on the band gap is also related with the size of nanoribbons; the wider the nanoribbon, the easier the modulation, and the smaller the critical electric field.