The antioxidant activities of flavonoids and their glycosides were measured with the 2,2-diphenyl-1-picrylhydrazyl radical (DPPH radical, DPPH(·)) scavenging method. The results show that free hydroxyl flavonoids are not necessarily more active than O-glycoside. Quercetin and kaempferol showed higher activity than apigenin. The C- and O-glycosides of flavonoids generally showed higher radical scavenging activity than aglycones; however, kaempferol C3-O-glycoside (astragalin) showed higher activity than kaempferol. In the radical scavenging activity of flavonoids, it was expected that OH substitutions at C3 and C5 and catechol substitution at C2 of B ring and intramolecular hydrogen bonding between OH at C5 and ketone at C3 would increase the activity; however, the reasons have yet to be clarified. We here show that the radical scavenging activities of flavonoids are controlled by their absolute hardness (η) and absolute electronegativity (χ) as a electronic state. Kaempferol and quercetin provide high radical scavenging activity since (i) OH substitutions at C3 and C5 strikingly decrease η of flavones, (ii) OH substitutions at C3 and C7 decrease χ and η of flavones, and (iii) phenol or o-catechol substitution at C2 of B ring decrease χ of flavones. The coordinate r(χ, η) as the electron state must be small to increase the radical scavenging activity of flavonoids. The results show that chemically soft kaempferol and quercetin have higher DPPH radical scavenging activity than chemically hard genistein and daidzein.