The antioxidant properties of coumarin derivatives using the 2,2ˈ -diphenyl-1- picrylhydrazyl (DPPH) radical scavenging assay were investigated by the application of Quantitative Structure Activity Relationship (QSAR) studies. The molecular structures were optimized and submitted for the generation of quantum chemical and molecular descriptors. Genetic Function Algorithm (GFA) was employed in model development. Also the applicability domain of the developed models were accessed by the leverage approach. The Variation Inflation Factor (VIF), Mean Effect (MF) and Degree of Contribution (DC) of these descriptors were estimated. Five predictive QSAR models were developed and subjected to various validation tests. The developed models gave highly encouraging results upon validation (R=0.938, R^2=0.879, Q^2=0.845, [R^2]_pred=0.700 and cR_p^2= 0.832. This research indicates that the most crucial descriptors that influence the free radical scavenging activities and essential in the design of new set of the coumarin antioxidants are the HBDCount (hydrogen-bond donor count), AATS3e (Average Broto-Moreau autocorrelation - lag 3 / weighted by Sanderson electronegativities), and the MW (Molecular weight) descriptors.