Krill byproduct was hydrolyzed with Alcalase 2.4L to produce functional ingredients for high antioxidative activities against 1,1-dimethyl-2-picryl-hydrazyl (DPPH) radical and Fe. The objective of this study was to investigate the optimum condition for degree of hydrolysis and antioxidative activity of enzymatic hydrolysate produced with the commercial Alcalase using response surface methodology (RSM) with a central composite rotatable design (CCRD). The ranges of independent variables were pH 7.6~10.4 for initial pH and $50.9{sim}79.1^{circ}C$ for hydrolysis temperature and their dependent variables were degree of hydrolysis, Brix, amount of phenolic compounds, DPPH-scavenging activity and Fe-chelating activity. RSM with CCRD was well designed to investigate the optimum condition for functional ingredients with high antioxidative activities using Alcalase 2.4L because of their high $R^2$ values of the range of 0.93~0.99 except the $R^2$ value of 0.50 for the amount of total phenolic compounds. The optimum hydrolysis conditions were pH 9.5 and $62^{circ}C$ for degree of hydrolysis (DH) and pH 9.1 and $64^{circ}C$ for DPPH-scavenging activity by response surface methodology. The yield of DH and DPPH-scavenging activity were $14.1{pm}0.5%$ and $10.5{pm}0.2%$, respectively. It is advantageous to determine the optimum hydrolysis conditions of krill and its by-products for the creation of different kinds of food products, as well as to increase the usage of marine protein sources.