Purple corn cob (Zea mays L.) extracts were obtained by sequential extraction in fixed bed, using GRAS solvents (Generally Recognized as Safe) ordered by increasing polarity, as follows: supercritical carbon dioxide (scCO2) (nonpolar) in a first step, ethanol (polarity 5.2) in a second step, and water (polarity 9.0) in a third step at the same conditions of temperature and pressure. CCRD (Central Composite Rotatable Design) was used to study the effect of pressure (259-541 bar) and temperature (36-64°C) on the following parameters: overall yield (X0) of each extraction step; yield and content of total monomeric anthocyanins (TMA), total phenolics (TP), and total flavonoids (TF); antioxidant activity (AA) expressed as effective concentration EC50/DPPH responsible for 50% decrease in the initial activity; color by CIELAB L∗a∗b∗system. Quantification of specific anthocyanins was performed by HPLC. The process was optimized using response surface methodology (RSM), and the best responses were: X0 of 15.4% in the 3rd step at 65°C and 440 bar; TMA of 64 mg cyanidin-3-glucoside per gram extract in the 2nd step at 45°C and 420 bar; TF of 93.7 mg catechin equivalents per gram extract obtained in the 3rd step at 50°C and 400 bar; TP of 389 mg gallic acid equivalents per gram extract, and AA (EC50/DPPH) of 21 μg/mL in the 2nd step at 65°C and 450 bar. The color of the extracts was affected by the type of solvent, and the highest cyanidin 3-glycoside concentration was observed in the 2nd extraction step, with values of 26-38 mg per gram extract, determined by HPLC.