The series of fifteen synthesized 4-hydroxycoumarin derivatives was subjected to antioxidant activity evaluation in vitro, through total antioxidant capacity, 1,1-diphenyl-2-picryl-hydrazyl (DPPH), hydroxyl radical, lipid peroxide scavenging and chelating activity. The highest activity was detected during the radicals scavenging, with 2b, 6b, 2c, and 4c noticed as the most active. The antioxidant activity was further quantified by the quantitative structure-activity relationships (QSAR) studies. For this purpose, the structures were optimized using Paramethric Method 6 (PM6) semi-empirical and Density Functional Theory (DFT) B3LYP methods. Bond dissociation enthalpies of coumarin 4-OH, Natural Bond Orbital (NBO) gained hybridization of the oxygen, acidity of the hydrogen atom and various molecular descriptors obtained, were correlated with biological activity, after which we designed 20 new antioxidant structures, using the most favorable structural motifs, with much improved predicted activity in vitro.