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Graphene has been considered as a candidate for interconnect metal due to its high carrier mobility and current drivability. In this letter, the breakdown mechanism of single-layer chemical-vapor-deposited (CVD) graphene and triple-layer CVD graphene has been investigated at three different conditions (air exposed, vacuum, and dielectric capped) to identify a failure mechanism. In vacuum, both single- and triple-layer graphenes demonstrated a breakdown current density as high as ~108 A/cm2, which is similar to that of exfoliated graphene. On the other hand, the breakdown current of graphene exposed to air was degraded by one order of magnitude from that of graphene tested in vacuum. Thus, oxidation initiated at the defect sites of CVD graphene was suggested as a major failure mechanism in air, while Joule heating was more dominant with dielectric capping and in vacuum.