Recently, low-cost, high-quality graphene can be obtained readily, so it is potential to prepare conductive graphene modified asphalts (GMAs). In this paper, GMAs were prepared with 0%, 2%, 4%, 6%, 8%, and 10% of graphene by weight of composites. Dynamic shear rheological experiments conducted from −30 to 120 °C illustrate that elasticity at above ambient temperatures and rutting resistance at higher temperatures are enhanced and, especially, the conceived percolation of GMAs occurs at graphene contents (GC) above 8% which were verified from three changes as GC increases, i.e., the curve characteristics of complex moduli, storage moduli at temperatures over 100 °C, temperatures when the phase angle reaches 90° and the trend of TG’=G’’. The modification mechanisms are different before and after percolation. Before the percolation threshold, graphene which has a molecular structure similar to asphaltene enhances asphalt, like increasing asphaltene components, and after threshold, graphene improves asphalt because of the formed graphene networks. Rotational viscosities test results show that the higher the GC is, the higher the operating temperatures are, but the operating temperatures are higher than 200 °C when GC is above 4%. The percolation helps to further develop conductive asphalt concrete for intelligence pavement, but the operating properties of GMAs need to be improved.