The structural stability and electronic properties of single-wall (SW) and double-wall (DW) ZnO nanotubes (NTs) are investigated by using the first-principle approaches. It shows that the stabilities of SW ZnO NTs increase as the size increases, while the stabilities of DW ZnO NTs are almost independent of the diameter and thickness. All the NTs show direct band gap semiconductor characteristics. The band gaps of DW NTs are larger than those of SW NTs and are almost independent of the diameter and thickness. The band gaps of ZnO NTs become larger than that of the corresponding bulk wurtzite ZnO due to quantum size effect.