In this research, the neutrase hydrolysis conditions of edible bird’s nest (EBN) by-products were optimized by response surface methodology (RSM). Antioxidant peptides were then isolated from the EBN by-products by ultrafiltration and chromatography taking the DPPH radical scavenging ability as an indicator. The antioxidant activity of the purified peptides was estimated by radical scavenging ability and sodium nitroprusside (SNP)-induced damage model in PC12 cells. When the enzyme concentration was10 kU/g-hydrolysis temperature was 45 °C, and hydrolysis time was 10.30 h, the degree of hydrolysis (DH) of EBN by-product hydrolysate (EBNH) was the highest. The purified peptide exerted strong scavenging ability with EC50 values of 0.51, 1.31, and 0.65 mg/mL for DDPH, ABTS, and O2− radicals, respectively. In addition, the purified peptides could significantly reduce the SNP-induced oxidative damage of PC12 cells, and twelve peptides that were rich in leucine (Leu), valine (Val), and lysine (Lys) were identified by LC-MS/MS. These results suggested that EBN by-products have potential as new materials for natural antioxidant peptides.