Localized Gaussian type orbital-periodic boundary condition-density functional theory (LGTO-PBC-DFT) method was used to determine the electronic and detailed geometrical structures of (n, 0) zigzag type for n = 6 – 33 and (n, n) armchair type for n = 3 – 15 single-walled boron-nitride (BN) nanotubes with infinite tubular lengths. The calculations reveal that the calculated Eg (band gap between HOCO and LUCO) increases with increasing tubular diameter and eventually converge to 5.03 eV for BN nanotubes of larger tubular diameter. According to the calculated Egs, the BN nanotubes are semi-conductor and their conductivities are not sensitive to the tubular diameter. Theoretically, the calculated bond length decreases with increasing tubular diameter. Based on our calculations, the bond length and angle do converge to 1.45 Å and 120 degree, respectively. Thus, the structures of BN nanotubes with the infinite tubular length approach the perfect hexagonal network when the tubular diameter increases. The calculated results also indicate that zigzag BN nanotubes with the tubular diameter larger than 18 Å display 3n properties in the calculated Eg, which is also obtained for zigzag carbon nanotubes.