The electrical properties of an epoxy resin filled with carbon fibers were studied. By discharging a high voltage through the composite it was found that the resistivity of the composite decreased. This effect was attributed to local dielectric breakdown of polymer layer between carbon fibers. The conduction mechanism of common and breakdown composites was studied by means of exploring of current-voltage characteristics and the frequency dependence of resistivity. A positive temperature coefficient (PTC) effect of resistivity behavior was observed both for common and breakdown samples.