Nitrogen-doped carbon nanotubes (NCNTs) are attractive for electrocatalytic applications in fuel cells due to their low cost and high electrocatalytic activity. By using density functional theory calculations, the electrocatalytic mechanisms of the oxygen reduction reaction (ORR) under electrochemical conditions are studied at graphite-like N groups (N_G) and pyridine-like N groups (N_P) of NCNTs, in which the effect of electrode potentials on the activation energy (E_a) and reaction energy (E_r) is taken into account. The ORR occurs at both N_G and N_P defect sites via two different four-electron OOH and two-electron H₂O₂ mechanisms. At the lower potential region, both mechanisms are simultaneously responsible for the reaction at N_G and N_P defect sites; while at higher potentials, the four-electron mechanism becomes dominant and the ORR at N_P defect sites is more energetically favorable than that at N_G defect sites.