Duck blood is rich in protein. It is one of the main by-products in the slaughter industry. The objective of this research was to optimize and establish a method for producing duck plasma antioxidant peptides. The composition of duck plasma powder was analyzed. Protease selection experiment (Alcalase, Protamex, and Flavourzyme) and single-factor experiment were performed, and response surface methodology was used to determine the optimal hydrolysis conditions for duck plasma. Among the proteases, Alcalase hydrolysate exhibited the strongest 1,1-diphenyl-2-picrylhydrazyl scavenging rate. The optimum enzymatic hydrolysis conditions were hydrolysis time of 6 h, temperature of 65.5°C, pH 10.0, and enzyme-to-substrate ratio of 0.3%. The 1,1-diphenyl-2-picrylhydrazyl scavenging rate reached 64.84%, and the ratio of essential amino acids was 38.76%. Briefly, the duck plasma hydrolysate exhibited strong antioxidant properties and reasonable composition of amino acids. Thus, it may be used as a nutritional or functional ingredient in foods or medicines. This research provides a theoretical basis for comprehensive processing and high value utilization of duck plasma.