GaN is known as the third generation of semiconductor and holds promising applications. In this present work, one-dimensional zigzag nanotubes derived from GaN are studied in depth, mainly focusing on their chemical bondings, electronic structures, transport properties, and the regulating effects under gate voltage for nanotubes doped with low-concentration non-metallic atoms in main-groups IIIA-VIIA. Some important findings are obtained, such as the chemical bonds around a heteroatom atom, and their average bond length, binding energy, and chemical formation energy are closely related to the atomic number (the atomic radius), and the charge transfer between heteroatom and nanotubes is directly related to their relative electronegativity. More importantly, we find that although the intrinsic nanotube is a semiconductor, when it is doped with non-metallic atoms, the electronic phase of nanotube possesses an obvious odd-even effect. Namely, after being doped by hetero-atoms in main-groups IIIA, VA, VIIA, nanotubes are semiconductors, but they becomes metals after having been doped with hetero-atoms in main-groups IVA and VIA. This phenomenon has a close relation with the lone-paired electronic state. And also, It is found that with atom doping, the difference between carriers’ mobilities (the hole mobility and electron mobility) of semiconducting tubes can be regulated to reach one order of magnitude, especially the hole mobility and electron mobility can be obviously enhanced by a higher gate voltage. For example, when the gate voltage is increased to 18 V, the hole mobility rises nearly 20 times compared with the case without gate voltage.