Based on the reported research, hydroxyl radicals can be rapidly transformed into carbonate radicals in the carbonate-bicarbonate buffering system in vivo. Many of the processes considered to be initiated by hydroxyl radicals may be caused by carbonate radicals, which indicates that lipid peroxidation initiated by hydroxyl radicals can also be caused by carbonate radicals. To date, theoretical research on reactions of hydrogen abstraction from and radical addition to polyunsaturated fatty acids (PUFAs) of carbonate radicals has not been carried out systematically. This paper employs (3Z,6Z)-nona-3,6-diene (NDE) as a model for polyunsaturated fatty acids (PUFAs). Density functional theory (DFT) with the CAM-B3LYP method at the 6-311+g(d,p) level was used to calculate the differences in reactivity of carbonate radicals abstracting hydrogen from different positions of NDE and their addition to the double bonds of NDE under lipid solvent conditions with a dielectric constant of 4.0 (CPCM model). Grimme's empirical dispersion correction was taken into account through the D3 scheme. The energy barrier, reaction rate constants, internal energy, enthalpy and Gibbs free energy changes in these reactions were calculated With zero-point vibrational energy (ZPVE) corrections. The results indicated that carbonate radicals initiate lipid peroxidation primarily through hydrogen abstraction from diallyl carbon atoms. The reaction of hydrogen abstraction from diallyl carbon atoms exhibits the highest reaction rate, with a reaction rate constant approximately 43-fold greater than the second-ranked hydrogen abstraction from allyl carbon atoms. This process has the lowest energy barrier, internal energy, enthalpy, and Gibbs free energy changes, indicating that it is also the most spontaneous process.