Anthracycline antibiotics, e.g., doxorubicin, daunomycin, and other anthraquinones, are an important family of antitumor agents widely used in chemotherapy, which is currently the principal method for treating many malignancies. Thus, development of improved antitumor drugs with enhanced efficacy remains a high priority. Interaction of anthraquinone-based anticancer drugs with cell membranes attracts significant attention due to its importance in the eventual overcoming of multidrug resistance (MDR). The use of drugs able to accumulate in the cell membrane is one of the possible ways of overcoming MDR. In the present work, the aspects of interaction of anthraquinone 2-phenyl-4-(butylamino)naphtho[2,3-h]quinoline-7,12-dione) (Q1) with a model membrane were studied by means of NMR and molecular dynamics simulations. A fundamental shortcoming of anthracycline antibiotics is their high cardiotoxicity caused by reactive oxygen species (ROS). The important feature of Q1 is its ability to chelate transition metal ions responsible for ROS generation in vivo. In the present study, we have shown that Q1 and its chelating complexes penetrated into the lipid membrane and were located in the hydrophobic part of the bilayer near the bilayer surface. The chelate complex formation of Q1 with metal ions increased its penetration ability. In addition, it was found that the interaction of Q1 with lipid molecules could influence lipid mobility in the bilayer. The obtained results have an impact on the understanding of molecular mechanisms of Q1 biological activity.