Carbon nanotube (CNT) has a great tolerance to high current density which is a cause of electromigration (EM). Therefore, CNT is expected to use as the materials of nanoscale components of electronic devices. The damage mechanisms of CNT are regarded as the effects of oxidation by Joule heating and/or the EM by high-density electron flows. In this study, we investigated the damage mechanism of CNT structures used as nano-component of electronic devices. An EM acceleration testing system was designed using the CNT structures collected at the gap of thin-film electrodes. The EM tests were conducted under the several kinds of current density conditions and the surrounding environments. An indicator of lifetime was determined by voltage measurements during the acceleration tests and their fracture phenomena were evaluated by means of microscopic observations. As the results, the amounts of lifetime of CNT were longer in the lower oxygen concentrations than in the air condition. In the microscopic studies, it was confirmed that the local evaporation of carbon atoms due to oxidation appeared at the cathode side of the CNT structures under low current density, and the center area of CNT under high current density. Both types of damage morphologies induced by oxidation and EM were observed at the damaged CNT. The results showed the dominant damage mechanism alternated between oxidation and EM depending on current density under oxygen rich conditions.