The present work regards the nonlinear electrical behavior of carbon fiber reinforced cement mortar in the dry state while the fiber content is near the percolation threshold. Tunneling effect theory and Ohm’s law were employed to interpret the conductive mechanism. An obvious flat zone was observed in the resistivity–voltage plot when applied voltage is low. The critical voltage beyond which the resistivity starts to deviate differs with varying fiber volume fractions. A mathematical model relating resistivity of cement-based composite and the electric field intensity was validated experimentally. Fitting results show that the influence of tunneling effect on the conductivity of the system decreases significantly owing to the increasing fiber content. Consequently, tunneling barrier is no longer a hindrance to the motion of charge carriers when fiber content is in the vicinity or above the percolation threshold.