The in vitro antioxidant activities of eight 3-carboxycoumarin derivatives were assayed by the quantitative 1,1-diphenyl-2-picrylhydrazil (DPPH•) radical scavenging activity method. 3-Acetyl-6-hydroxy-2H-1-benzopyran-2-one (C1) and ethyl 6-hydroxy-2-oxo-2H-1-benzopyran-3-carboxylate (C2) presented the best radical-scavenging activity. A quantitative structure-activity relationship (QSAR) study was performed and correlated with the experimental DPPH• scavenging data. We used structural, geometrical, topological and quantum-chemical descriptors selected with Genetic Algorithms in order to determine which of these parameters are responsible of the observed DPPH• radical scavenging activity. We constructed a back propagation neural network with the hydrophilic factor (Hy) descriptor to generate an adequate architecture of neurons for the system description. The mathematical model showed a multiple determination coefficient of 0.9196 and a root mean squared error of 0.0851. Our results shows that the presence of hydroxyl groups on the ring structure of 3-carboxy-coumarins are correlated with the observed DPPH• radical scavenging activity effects.