Antioxidants, which can activate the body’s antioxidant defence system and reduce oxidative stress damage, are important for maintaining free radical homeostasis between oxidative damage and antioxidant defence. Six antioxidant peptides (P1–P6) were isolated and identified from the enzymatic hydrolysate of tilapia skin by ultrafiltration, reversed-phase high-performance liquid chromatography (RP-HPLC) and liquid chromatography–tandem mass spectrometry (LC–MS/MS). Moreover, the scavenging mechanism of the identified peptides against DPPH (2,2-Diphenyl-1-picrylhydrazyl) and ABTS (2-azido-bis (3-ethylbenzothiazoline-6-sulfonic acid) was studied by molecular docking. It was found that Pro, Ala and Tyr were the characteristic amino acids for scavenging free radicals, and hydrogen bonding and hydrophobic interactions were the main interactions between the free radicals and antioxidant peptides. Among them, the peptide KAPDPGPGPM exhibited the highest DPPH free radical scavenging activity (IC50 = 2.56 ± 0.15 mg/mL), in which the hydrogen bond between the free radical DDPH and Thr-6 was identified as the main interaction, and the hydrophobic interactions between the free radical DDPH and Ala, Gly and Pro were also identified. The peptide GGYDEY presented the highest scavenging activity against ABTS (IC50 = 9.14 ± 0.08 mg/mL). The key structures for the interaction of this peptide with the free radical ABTS were identified as Gly-1 and Glu-5 (hydrogen bond sites), and the amino acids Tyr and Asp provided hydrophobic interactions. Furthermore, it was determined that the screened peptides are suitable for applications as antioxidants in the food industry, exhibit good water solubility and stability, are likely nonallergenic and are nontoxic. In summary, the results of this study provide a theoretical structural basis for examining the mechanism of action of antioxidant peptides and the application of enzymatic hydrolysates from tilapia skin.