Downsizing electronic and electric equipment requires the optimization of electric field distributions in order to avoid localized dielectric breakdown (also called partial discharges). This paper presents a novel dielectric composite material aimed at grading electrical local surface stress. This functional material has a conductivity which increases by several orders with the applied electric field giving the ability to distribute the field by itself. It is prepared for the first time by dispersing graphite nanoplatelets in a polymer and may be used as a resistive or capacitive field grading material in electronic and electrical applications. Mechanisms at the origin of the nonlinear behavior are discussed.