A new method for measuring the antioxidant power of wine has been developed based on the accelerated electrochemical oxidation of 2,2'-azino-bis(3-ethylbenzthiazoline-6-sulfonic acid) (ABTS). The calibration (R = 0.9922) and repeatability study (RSD = 7%) have provided good statistical parameters. The method is easy and quick to apply and gives reliable results, requiring only the monitoring of time and absorbance. It has been applied to various red and white wines of different origins. The results have been compared with those obtained by the total antioxidant status (TAS) method. Both methods reveal that the more antioxidant wines are those with higher polyphenolic content. From the HPLC study of the polyphenolic content of the same samples, it is confirmed that there is a positive correlation between the resveratrol content of a wine and its antioxidant power.