Phenolic acids are naturally occurring compounds that are known for their antioxidant and antiradical activity. We present experimental and theoretical studies on the antioxidant potential of the set of 22 phenolic acids with different models of hydroxylation and methoxylation of aromatic rings. Ferric reducing antioxidant power assay was used to evaluate this property. 2,3-dihydroxybenzoic acid was found to be the strongest antioxidant, while mono hydroxylated and methoxylated structures had the lowest activities. A comprehensive structure–activity investigation with density functional theory methods elucidated the influence of compounds topology, resonance stabilization, and intramolecular hydrogen bonding on the exhibited activity. The key factor was found to be a presence of two or more hydroxyl groups being located in ortho or para position to each other. Finally, the quantitative structure–activity relationship approach was used to build a multiple linear regression model describing the dependence of antioxidant activity on structure of compounds, using features exclusively related to their topology. Coefficients of determination for training set and for the test set equaled 0.9918 and 0.9993 respectively, and Q2 value for leave-one-out was 0.9716. In addition, the presented model was used to predict activities of phenolic acids that haven’t been tested here experimentally.