In this study, the peach kernel proteins were extracted and treated with alkaline proteinase to generate peach kernel protein hydrolysate (PKH), which showed angiotensin converting enzyme (ACE) inhibition activity. The hydrolysate was separated into four fractions and their anti-ACE activities were investigated. Our results showed that all PKHs had anti-ACE activity, and the lowest molecular weight fraction PKH4 had the highest ACE inhibitory activity. Lineweaver–Burk plots illustrated that the inhibition types of PKH3 and PKH4 were non-competitive. The Ki of PKH4 was lower than Ki of PKH3; suggesting PKH4 had high affinity to ACE. Amino acid composition analysis showed that the best anti-ACE peptide PKH4 possessed high levels of hydrophobic amino acids, branched-chain amino acids, and aromatic amino acids. In summary, our findings demonstrated that high anti-ACE activity is negatively related to the size of the PKHs and possibly the composition of amino acids, and the PKH4 was the best ACE inhibitor. Further, peach kernel peptides can be developed as a functional food for patients with hypertension.