Polypeptide-based materials are used as building blocks for drug delivery systems aimed at toxicity decrease in chemotherapeutics. A molecular-level approach is adopted for investigating the non-covalent interactions between doxorubicin and a recently synthesized drug-binging peptide as a key part of a system for delivery to neoplastic cells. Molecular dynamics simulations in aqueous solution at room and body temperature are applied to investigate the structure and the binding modes within the drug–peptide complex. The tryptophans are outlined as the main chemotherapeutic adsorption sites, and the importance of their placement in the peptide sequence is highlighted. The drug–peptide binging energy is evaluated by density functional theory calculations. Principal component analysis reveals comparable importance of several types of interaction for the binding strength. π-Stacking is dominant, but other factors are also significant: intercalation, peptide backbone stacking, electrostatics, dispersion, and solvation. Intra- and intermolecular H-bonding also stabilizes the complexes. The influence of solvent molecules on the binding energy is mild. The obtained data characterize the drug-to-peptide attachment as a mainly attractive collective process with interactions spanning a broad range of values. These results explain with atomistic detail the experimentally registered doxorubicin-binging ability of the peptide and outline the complex as a prospective carrying unit that can be employed in design of drug delivery systems.