The optimized structures of some radical adducts of 5,5-dimethyl-1-pyrroline N-oxide were computed by different methods on ESR spectra. As trapped radicals, H, N-3, NH2, CH3, CCl3, OOH in water and F, OH, CF3, CH2OH, OC2H5 in benzene solutions were used. The calculated isotropic hyperfine coupling constants of all the trapped radicals were compared with the corresponding experimental data. The hyperfine coupling constant due to the beta proton of the nitroxide radical was seen to be consist with the McConnel's relation alpha(beta) = B (0) + B (1)cos(2)theta and, to be effected with the opposite spin density of oxygen nucleus bonded to the nitrogen. It was concluded that in hyperfine calculations the DFT(B3PW91)/LanL2DZ level is superior computational quantum model relative to the used other level. Also, the study has been enriched by the computational of the optimized geometrical parameters, the hyper conjugative interaction energies, the atomic charges and spin densities for all the radical adducts.