In this study, high-energy ball milling accompanied by compaction and sintering were employed for manufacturing Cu-based hybrid nanocomposite reinforced by Al2O3 and GNPs. This hybrid nanocomposite is proposed to meet the specification of heat sink applications, where excellent mechanical and thermal performance is demanding. Different processing parameters were experimentally considered such as sintering temperature and weight percentage of GNPs, 0, 0.25, 0.50, 0.75, and 1 wt %. The weight percentage of Al2O3 was fixed at 10%. The results demonstrated that the mechanical and thermal performance of the fabricated nanocomposites were superior for nanocomposite containing 0.5% GNPs and sintered at 1000 ◦C. The hardness, the thermal conductivity and the coefficient of thermal expansion (CTE) were improved by 21%, 16.7%, and 55.2%, respectively, compared to composite without GNPs addition. The improved mechanical and thermal properties were attributed to the low stacking fault energy, small crystallite size, high dislocation density, and low lattice strain of the composite prepared at this composition. Moreover, the better dispersion of the nano-particles of GNPs and Al2O3 inside the matrix helped for the strength and thermal conductivity improvement while maintaining low CTE.