In order to improve electric-tree resistant performance and dielectric breakdown strength of ethylene-propylene-diene misch-polymere (EPDM) material used for cable accessory reinforce insulation, the two specific aromatic ketone compounds—vinylphenylacetone (VPE) and 4-propylene oxyxy-2-hydroxydibenzenone (AOHBP) are employed as two paradigms of voltage stabilizer for chemical-graft modifications. Electric-tree resistances and insulation performances of modified EPDM materials and their charge trapping mechanism of thermoelectron inhibitions are studied by the accelerated electric-tree aging experiments, alternating current (AC) dielectric breakdown tests, surface potential trap-level analyses and first-principles calculations. Both the two species of voltage stabilizers are effective for promoting electric-tree inception voltage and dielectric breakdown strength, leading to a high extension of electric-tree morphology and smaller dimension of electric-trees growth, in which AOHBP is more significant. The two species of voltage stabilizers have been successfully grafted onto EPDM molecular-chains in thermal-chemistry crosslinking reactions of EPDM, introducing multiple shallow levels of charge traps, which reduces the energy released by trapping charge carriers and thus alleviates electric-tree aging of EPDM. The AOHBP and VPE represent a high electron affinity and a small electronic energy gap, which is competent of assimilating the kinetic energies of hot charge carriers whilst restricting Auger electronic excitation. Especially, the benzene group in voltage stabilizer renders shallow level charge traps with a larger carrier capture cross-section than deep traps and simultaneously possesses the high atomic vibration frequencies similar as electronic-transition energies, which results in effective dissipation on the kinetic energies of hot charge carriers. This mechanism dominates to increase electric-tree resistance and insulation strength of EPDM. The present study proves the important role of voltage stabilizers in improving insulation performance of EPDM material, and reveals the refrigeration mechanism on hot charge carriers for restricting electric-tree growth, which provides a significant strategy of chemical modifications for developing high-insulation cable accessory materials.