The effects of three types of free radical scavengers such as N, N'-di-sec-butyl-p-phenylenediamine (44PD), tert-butylhydroquinone (TBHQ) and diisopropyl xanthate disulfide (DIP) on the structural evolution and properties changes of ethylene vinyl acetate copolymers (EVA) under γ-ray irradiation were investigated. Thermogravimetric analysis (TGA) results showed that the free radical scavengers could inhibit the cleavage of polyethylene chain segments in EVA at higher absorbed doses. The results of gel content and stress relaxation tests showed that the three antioxidants or stabilizers could inhibit the construction of the internal cross-linking structure of EVA, in which the inhibitory effect of the amine antioxidant 44PD was relatively insignificant. However, when the absorbed dose was higher, the EVA containing the free radical scavenger had a more complete cross-linking structure and a lower rate of stress relaxation. The mechanical properties test results indicate that all three free radical scavenger can inhibit the irradiation-induced aging of EVA, among which DIP is more effective. The retention rate of the elongation at break of EVA at an absorbed dose of 500 kGy is 68%, while a retention rate of 96% of the elongation at break is reached at the same absorbed dose with the addition of 1% DIP.