To optimize the hydrolysis conditions in the production of antioxidant hydrolysates from tuna cooking juice concentrate (TC) to maximize the 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical scavenging activity, TC containing 48.91% protein was hydrolyzed with Alcalase 2.4 L, and response surface methodology (RSM) was applied. The optimum hydrolysis conditions included a 2.2% (w/v) Alcalase concentration and 281 min hydrolysis time, resulting in the highest DPPH radical scavenging activity of 66.49% (0.98 µmol Trolox/mg protein). The analysis of variance for RSM showed that hydrolysis time was an important factor that significantly affected the process (p < 0.05). The effects of different drying methods (freeze drying, hot air drying, and vacuum drying) on the DPPH radical scavenging activity and amino acid (AA) profiles of TC hydrolysate (TCH) were evaluated. Vacuum-dried TCH (VD) exhibited an increase in DPPH radical scavenging activity of 81.28% (1.20 µmol Trolox/mg protein). The VD samples were further fractionated by ultrafiltration. The AA profiles and antioxidant activities in terms of the DPPH radical scavenging activity, 2,2'-azino-bis(3-ethylbenzthiazoline)-6-sulfonic acid (ABTS) radical scavenging activity, ferric reducing antioxidant power, and ferrous ion chelating activity were investigated. Glutamic acid, glycine, arginine, and cysteine were the major AAs found in the TCH fractions. The highest DPPH radical scavenging activity was found in the VD-1 fraction (< 5 kDa). The VD-3 fraction (> 10 kDa) exhibited the highest ABTS radical scavenging activity and ferric reducing antioxidant power. The ferrous ion chelating activity was the highest in VD-1 and VD-2 (5 to 10 kDa). In conclusion, this study provided the optimal conditions to obtain high antioxidant activities through TCH production, and these conditions could provide a basis for the future application of TCH as a functional food ingredient.