Purple sweet potato extract is a rich source of anthocyanins, which have been attributed to have great health benefits. The objective of the study was to apply the response surface methodology to obtain the best extraction parameters of temperature, pH and ethanol: water. There were 11 experiment carried out with 3 central points. The dependent variables investigated were temperature (50 – 65 - 80°C), concentration of the solvent etanol : water (55% - 75% - 95%) and pH (2 - 4 - 6) and the independent variables were the extraction time (1 hour), sample proportion lyophilized with the extracting solvent (g / mL) of 1:10. Statistical analysis was performed using the Statistic version 5.0 program. The statistical model determined to obtain the extraction of the highest content of totais monomeric anthocyanins was expressed in the AMT equation (mg eq cy-3-glu / 100gEL) = 143.7 + 33.0 (Temperature) - 52.0 (Ethanol) - 56.75 (pH) + 13.0 (Temperature) (Ethanol) - 8.5 (Temperature) (pH) + 34.25 (Ethanol) (pH). The proposed model was mathematically satisfactory, as they presented high regression coefficients. The optimal extraction conditions were 55% ethanol, pH 2 at 80 ºC, the value of total monomeric anthocyanins was 341.85mg / 100gEL on a dry basis. The main effects and their interactions were tested by ANOVA, where it was verified that the variables of pH extraction and ethanol concentration showed to be statistically significant at 90% of the confidence level and the statistical R indicated that the model explains 84.57 % of the variation, suggesting that the increase of the pH and concentration of ethanol damages the extraction of anthocyanins.