Cryotin F could be used for hydrolyzing shrimp byproducts into bioactive ingredients, which could be used as value-added products. The objective of this study was to investigate the optimum condition for antioxidative activities of the enzymatic hydrolysate produced with Cryotin F using response surface methodology with central composite rotatable design. Shrimp byproducts (shells and heads) were hydrolyzed with Cryotin F. The experimental ranges of the independent variables for 20 experimental runs were 28.2-61.8${^{circ}C}$ reaction temperature, pH 6-10 and 0.5-5.5% enzyme concentration. The degree of hydrolysis for the reaction products was measured. Their antioxidative activities were measured using 1,1-diphenyl-2-picryl-hydrazyl (DPPH) scavenging activity and Fe-chelating activity. The experimental method with central composite rotatable design was well designed to investigate the optimum condition for biofunctional ingredients with antioxidative activities using Cryotin F because of their high R2 values of 0.97 and 0.95 for DPPH-scavenging activity and Fe-chelating activity, respectively. Change in enzyme concentration did not significantly affect their antioxidative activities (p<0.05). Both DPPH scavenging activity and chelating activity against Fe for the enzyme hydrolysates were more affected by the pH of enzyme hydrolysis than by their action temperature. DPPH-scavenging activity was higher at acidic pH than alkali pH, while chelating activity against Few was inversely affected. Hydrolysate of shrimp byproducts showed high antioxidative activities depending on the treatment condition, so the optimum treatment of enzymatic hydrolysate with Cryotin F and other proteases can be applied to shrimp byproducts (shells) and other protein sources for biofunctional ingredients.