In this study, naked oat bran albumin hydrolysates (NOBAH) were subjected to gel chromatography with Sephadex G-15, reverse phase-high liquid performance separation, and UPLC-ESI-MS/MS identification. Six safe peptides including Gly-Thr-Thr-Gly-Gly-Met-Gly-Thr (GTTGGMGT), Gln-Tyr-Val-Pro-Phe (QYVPF), Gly-Ala-Ala-Ala-Ala-Leu-Val (GAAAALV), Gly-Tyr-His-Gly-His (GYHGH), Gly-Leu-Arg-Ala-Ala-Ala-Ala-Ala-Ala-Glu-Gly-Gly (GLRAAAAAAEGG), and Pro-Ser-Ser-Pro-Pro-Ser (PSSPPS) were identified. Next, in silico screening demonstrated that QYVPF and GYHGH had both angiotensin-I-converting enzyme (ACE) inhibition activity (IC50: 243.36 and 321.94 μmol/L, respectively) and Zinc-chelating ability (14.85 and 0.32 mg/g, respectively). The inhibition kinetics demonstrated that QYVPF and GYHGH were both uncompetitive inhibitors of ACE. Molecular docking showed that QYVPF and GYHGH could bind, respectively, three and five active residues of ACE with short hydrogen bonds (but not belonging to any central pocket). QYVPF and GYHGH could bind, respectively, twenty-two and eleven residues through hydrophobic interactions. Moreover, GYHGH was able to affect zinc tetrahedral coordination in ACE by interacting with His383. The inhibition activities of QYVPF and GYHGH toward ACE were relatively resistant to gastrointestinal digestion. GYHGH improved zinc solubility in the intestines (p> 0.05) because its amino and carboxyl groups were chelating sites for zinc ions. These results suggest the potential applications of naked oat peptides for potential antihypertension or zinc fortification.