By using the tight-binding energy band theory, we study the band structures of BC3 nanotubes under stretching and compressing deformations, the conductivity band turns more and more close to the valence band of the BC3 nanotubes and eventually they overlap each other with the increase of tension. Furthermore, the results obtained show that the overlap under compressing is bigger than that under stretching. The biggest overlap under compressing is up to 05 eV, but it is only 02 eV under stretching. In addition, for armchair BC3 nanotubes, the results of band structures show that with the increase of tension, the BC3 nanotube transforms into an indirect semiconductor from a direct semiconductor, and then leads to the band overlap. The armchair BC3 nanotube is an unstable narrow-gap semiconductor, because a little compress (et=-0003) can convert it transform into an indirect semiconductor from a direct semiconductor. For zigzag BC3 nanotubes, a slight deformation can turn into a direct semiconductor having only one allowed wave vector from a direct semiconductor having all wave vectors, owing to the existence of two flat conductivity and valence bands.