By performing first principles electronic structure calculations, we have revealed the effect of boron/nitrogen pairs doping in armchair single-walled carbon nanotubes (SWCNT). It is shown that for two kinds of sites in the armchair SWCNT, the doping of B/N pairs can more easily happen on the P1 site which is at 30° angle to the tube axis. An energy gap is opened in metallic SWCNT by doping B/N pairs, and the energy gap increases with raising the axial concentration of the B/N pairs. Moreover, when two couples of B/N pairs are doped in SWCNT, the electronic structure is sensitive to the relative positions of B/N pairs in the couple along the circumference of tubes. It’s due to that the original charge distribution is changed by B/N pairs doping, and the effect of B/N pairs is localized. When the distance between B/N pairs increases, the extent of the effect is increased. This result may contribute to preparing pure semiconductor and effectively controlling the electronic structure.