The surging demand for miniaturized compact devices has generated the need for new metal conductors with high current carrying ampacity, electric and thermal conductivity. Herein, we report carbon-metal conductors that exhibit a high breakdown current density (39% higher than copper) and electrical conductivity (e.g. 63% higher than that of copper at 363 K) in a broad temperature range. The mechanistic studies of thermal conductivity through first-principle modeling show that the multilayer graphene percolation networks efficiently decrease the electron-phonon coupling in the copper-graphene composites, even if phonon modes are activated at a high temperature. These results imply that the copper-based composites have the potential to be the next generation metal conductor with high electrical and thermal conductivity, as well as excellent current-carrying ampacity. More importantly, the developed composite can be deployed in the ink form, making it possible to be utilized by the microelectronic fabrication process.