The understanding of the structural requirements and the intermolecular-interaction mechanism are important for discovering potent angiotensin-converting enzyme (ACE) inhibitory peptides. In this study, we modified an egg-white derived peptide, LAPYK, using the amino acids with different properties to produce the LAPYK-modified peptides. The ACE inhibitory activities of the modified peptides were determined to explore the structural requirements of ACE inhibitory peptides (ACEIPs). Molecular simulation and isothermal titration calorimetry analysis were used to investigate interactions between the peptides and ACE. We found that hydrophobicity and the amino acids with ring structures were beneficial for the ACE inhibitory activities of the peptides. The results of the molecular mechanics poisson boltzmann surface area (MMPBSA) binding free energy calculations indicated that the polar solvation free energy (ΔGpolar) of the charged peptides (LAPYK, LAPYE) were unfavorable for binding to ACE. On the other hand, the results of isothermal titration calorimetry analyses suggested that the enthalpy-driven ACE-peptide interactions were more favorable than the entropy-driven ACE-peptide interaction counterparts.