The splitting of band structure and absorption spectrum, for boron nitride nanotubes (BNNTs) under axial magnetic field, is studied using the tight binding approximation. It is found that the band splitting ( at the point is linearly proportional to the magnetic field (. Our results indicate that the splitting rate , of the two first bands nearest to the Fermi level, is a linear function of n−2 for all (n,0) zigzag BNNTs. By investigation of the dependence of band structure and absorption spectrum to the magnetic field, we found that absorption splitting is equal to band splitting and the splitting rate of band structure can be used to determine the splitting rate of the absorption spectrum.