A novel architecture of 3D graphene growth on porous Al2O3 ceramics is proposed for thermal management using ambient pressure chemical vapor deposition. The formation mechanism of graphene is attributed to the carbothermic reduction occurring at the Al2O3 surface to initialize the nucleation and growth of graphene. The graphene films are coated on insulating anodic aluminum oxide (AAO) templates and porous Al2O3 ceramic substrates. The graphene coated AAO possesses one-dimensional isolated graphene tubes, which can act as the media for directional thermal transport. The graphene/Al2O3 composite (G-Al2O3) contains an interconnected macroporous graphene framework with an extremely low sheet electrical resistance down to 0.11 Ω sq−1 and thermal conductivity with 8.28 W m−1 K−1. The G-Al2O3 provides enormous conductive pathways for electronic and heat transfer, suitable for application as heat sinks. Such a porous composite is also attractive as a highly thermally conductive reservoir to hold phase change materials (stearic acid) for thermal energy storage. This work displays the great potential of CVD direct growth of graphene on dielectric porous substrates for thermal conduction and electronic applications.