The objective of this study was to apply the statistical technique known as response surface methodology (RSM) to model the free radical scavenging activity of mixtures of three antioxidant compounds, using 2,2-diphenyl-1-picrylhydrazyl (DPPH•). α-Tocopherol showed the highest antioxidant power (EC50) while ascorbic acid showed maximum antiradical efficiency. Reduced glutathione was not effective using the DPPH• system. The binary and ternary mixture effects were evaluated considering percentage reduction in [DPPH•] and the time needed to reach this reduction caused by addition of each mixture at 1.0 mM concentration. Although the surface curves have shown significant interactions, no combination between the compounds resulted in a greater percentage reduction in [DPPH•]/min than that shown by ascorbic acid alone. Both polynomial regressions were statistically significant with elevated adjusted R2. This study showed that RSM can be applied to predict the free radical scavenging activity of mixtures of antioxidants using the stable DPPH• as a free radical.