Ethylene-vinyl acetate copolymer (EVA) was functionalized to varying degrees with acrylonitrile (AN) by melt grafting processes. Fourier transform infrared spectra (FT-IR) confirmed that AN was successfully grafted onto the EVA. High resistance meter, electronic universal testing machine, etc. have studied the influencing factors of grafting process and the effect of grafting rate on oil resistance, mechanical properties and electrical properties. The results show that the optimal grafting process is that the dosage of AN is 8.0 wt%, the dosage of styrene (St) is 5.0 wt%, the dosage of Dilauroyl peroxide(LPO) is 0.4 wt% of the total amount of AN and St, and the grafting rate is 1.24%. With the increase of the amount of LPO and AN, the grafting rate first increased and then decreased. The grafting rate increases, so that the oil resistance, volume resistivity, and breakdown field strength of the grafted product are gradually increased. When the grafting rate is 1.24%, the volume resistivity is 1.63×1013 Ω·m, which is significantly improved compared with pure EVA, and the breakdown field strength is 23.26 kV/mm, which is 12.3% higher than pure EVA.