The conductive mechanism of nonlinear conductive behavior in conductive asphalt concrete is not clear. Based on the laboratory-prepared carbon fiber (CF)-carbon fiber powder (CFP) conductive asphalt concrete, the nonlinear conductive behavior of conductive asphalt concrete was investigated by testing the relationship of the external force field on the electrical resistivity of conductive asphalt concrete, and by combining the linear stochastic resistor network model, dynamic stochastic resistor network model, and nonlinear stochastic dynamic resistor model, to clarify the conductive mechanism of the nonlinear conductive behavior. The results showed that with the increase of carbon fiber content, asphalt-aggregate ratio and pressure, the resistivity shows a significant and similar nonlinear downward trend, and the increase of carbon fiber powder content leads to the first decrease and then increase of resistivity, and the volt-ampere characteristic curves of conductive asphalt concrete with different contents show nonlinear characteristics. Under the strong electric field, the nonlinear conductive behavior of the conductive phase material itself and the nonlinear conductive behavior caused by the conduction of the carrier channel in the insulating state together lead to the nonlinear conductivity behavior of the carbon fiber-carbon fiber powder conductive asphalt concrete, and it is proved that the tunneling effect exists in the conductive asphalt concrete under the electric field.