Ab initio calculations have been performed for determining structural stabilities of nitrogen-doped ultrathin single-walled boron nanotube. We have considered ultrathin boron nanotubes of diameters <0.5 nm, which include mainly three conformations of BNTs viz. zigzag (5,0), armchair (3,3) and chiral (4,2) with diameters 4.60, 4.78 and 4.87 angstrom, respectively. It has been investigated that alpha-BNTs are highly stable, while hexagonal BNTs are found to be least stable. In view of increasing structural stability of hexagonal BNTs, substitutional doping of foreign atoms, i.e. nitrogen is chosen. The nitrogen atoms substitute the host atoms at the middle of the tubes. The substitution doping is made with all the three conformations. The structural stabilities of BNTs have been investigated by using density functional theory (DFT). Subsequently, the cohesive energy is calculated, which directly measures the structural stability. The cohesive energy of BNTs has been calculated for different nitrogen concentrations. We found that the structures get energetically more stable with increasing nitrogen concentration. Moreover, it is also revealed that all the three BNTs are almost equally stable for single-atom doping, while the armchair BNT (3,3) is highly stable followed by zigzag (5,0) and chiral (4,2) BNTs for two-and three-atom doping. The structural stability is an important factor for realization of any physical device. Thus, these BNTs can be used for field emission, semiconducting and highly conducting devices at nanoscale.