Ab initio elongation method calculations have been performed on the electronic structures of the single-wall pristine boron nitride (BN) and boron nitride−carbon (BN/C) heterostructured nanotubes. This work is a first step toward the application of the elongation method to nanotube systems. For different kinds of BN and BN/C nanotubes, the errors per atom introduced by the elongation method are negligibly small and closed to 10−8 au, which indicates that elongation method is reliable for the investigation of BN nanotubes systems. Moreover, the carbon-doped effect on the nonlinear optical (NLO) properties of a BN nanotube is investigated. It is found that the α and γ values of armchair BN/C heterostructured nanotubes may be tuned by controlling the carbon content. With the increase of the concentration of carbon, the corresponding α and γ values of BN/C nanotubes increase. It will be useful for the designing of NLO materials.