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Abstract Resistive Field Grading Materials (RFGM) are used in critical regions in the electrical insulation system of high-voltage direct-current cable systems. Here, we describe a novel type of RFGM, based on a percolated network of zinc oxide (ZnO) tetrapods in a rubber matrix. The electrical conductivity of the composite increases by a factor of 108 for electric fields > 1 kV mm−1, as a result of the highly anisotropic shape of the tetrapods and their significant bandgap (3.37 eV). We demonstrate that charge transport at fields < 1 kV mm−1 is dominated by thermally activated hopping of charge carriers across spatially, as well as energetically, localized states at the ZnO–polymer interface. At higher electric fields (> 1 kV mm−1) band transport in the semiconductive tetrapods triggers a large increase in conductivity. These geometrically enhanced ZnO semiconductors outperform standard additives such as SiC particles and ZnO micro varistors, providing a new class of additives to achieve variable conductivity in high-voltage cable system applications.