Conductive polymer composites require a three-dimensional 3D network to impart electrical conductivity. A general method that is applicable to most polymers for achieving a desirable graphene 3D network is still a challenge. We have developed a facile technique to fabricate highly electrical conductive composite using vacuum-assisted infusion of epoxy into graphene sponge GS scaffold. Macroscopic GSs were synthesized from graphene oxide solution by a hydrothermal method combined with freeze drying. The GS/epoxy composites prepared display consistent isotropic electrical conductivity around 1 S/m, and it is found to be close to that of the pristine GS. Compared with neat epoxy, GS/epoxy has a 12-orders-of-magnitude increase in electrical conductivity, attributed to the compactly interconnected graphene network constructed in the polymer matrix. This method can be extended to other materials to fabricate highly conductive composites for practical applications such as electronic devices, sensors, actuators, and electromagnetic shielding.