Finite nitrogen-doped carbon nanotubes (NCNTs) with and without adsorbed O₂ were systematically investigated using the B3LYP/6-31G* method. NCNTs with 10 different lengths and 9 different diameters were considered. The charge carried by the N atom and its circumjacent C atoms, the HOMO–LUMO gap, the O₂ binding energy and the C–O bond length oscillate periodically as the tube length increases, whereas these values show a monotonic increase or decrease as the tube diameter is enlarged. All of the adsorbed oxygen investigated here is activated. Enlarging the tube diameter has a complicated influence on the catalytic ability of the NCNT. First, O₂ adsorption becomes increasingly difficult on the surface of the NCNT, and the reactivity of the O_a atom becomes lower and lower as the tube diameter is enlarged, which reduces the reactivity of the NCNT. Second, enlarging the tube diameter creates more active centers for the adsorption and activation of oxygen, which will increase the reactivity of the NCNT.