Grape pomace is a food industry residual material which may contain a high load of polyphenolic antioxidants and a number of methods have been implemented for their effective recovery. Nevertheless, eco-friendly processes should embrace environmentally benign and non-toxic solvents. On this basis, this study investigated the extraction of antioxidants, by employing aqueous acetic acid and citric solutions and monitoring the reducing power (P_R) of the extracts. The scope was to evaluate the effect of acid concentration on the extraction yield using kinetics. The kinetic model established allowed for the credible comparison of the extraction efficiencies, achieved with acetic acid and citric acid solutions of variable concentration. The results suggested that citric acid solutions were more effective in recovering red grape pomace antioxidants. Using a 4% (w/v) citric acid solution, a maximum P_R of 229.8 μM ascorbic acid equivalents per g of dry pomace could be attained. This investigation demonstrated that aqueous media used for the extraction of antioxidant compounds from food industry wastes could be significantly influenced by the acidifying agent and its concentration.