In this study, the reaction mechanism of the graft polymerization by cold plasma was investigated The plasma reactor was an electrodeless inductively coupled radio frequency system operating at 13.56MHz, which was employed in the tubular reaction chamber. The chemical structure of the acrylic acid grafts were investigated by ATR FT-IR. The intensity due to the methylene group increased by 2 or 3 times that of the untreated PET, and it is apparent due to the methylene group in the acrylic acid grafts. The hydroxyl group markedly increased also. It is mainly due to carboxylic acid stoup of the grafts and hydrogen bonded water affect on that. Also, we detected the peroxides of carbonyl group and carboxylic acid group at around 1755cm-1. The total reaction rate of the graft polymerization was related to the monomer pressure and in reverse proportion to the content of air or 02 in the system. It was also related to the electron density [e+] and the production yield of polymer radicals [∮] and the substantivity factor [$delta$] of a given polymer.