By using first principles calculation based on density functional theory, band structures, densities of states and electron density differences for an ideal (6, 0) ZnO nanotube (ZnONT), Al doped, N doped and Al, N co-doped nanotubes are investigated. The calculated results reveal that the doped nitrogen atom results in the formation of acceptor level in the band gap of the ZnONT, which indicates that the doped nanotube has the characteristic of a p-type semiconductor. While the high locality of the acceptor level leads to a lower solubility for the doped nitrogen atoms, the acceptor level is broadened and shows delocalizing characteristics in nanotube with Al, N co-doped. This co-doping may be an efficient method of preparing p-type ZnONTs.