Carbon fiber/graphene conductive asphalt mortar and asphalt concrete was prepared in the laboratory, the conductivity and conduction behavior of carbon fiber/graphene conductive asphalt mortar and asphalt concrete and the correlation between its resistance and applied voltage were studied. Through the research of the voltammetric characteristic curve, it is shown that the asphalt mortar and concrete has obvious nonlinear conduction behavior. The resistivity decreases significantly with the increase of voltage. The degree of nonlinearity gradually decreases with the increase of the amount of conductive filler. Using the dynamic random resistor network model, it is proved that the tunneling effect is the main cause of this nonlinear behavior. Under strong enough voltage, the partial carrier in the insulating region will be arranged to form the additional conductive path.