A cell-penetrating peptide (CPP) is a short amino-acid sequence capable of efficiently translocating across the cellular membrane of mammalian cells. However, the potential of CPPs as a delivery vector is hampered by the strong reduction of its translocation efficiency when it bears an attached molecular cargo. To overcome this problem, we used previously developed diblock copolymers of elastin-like polypeptides (ELPBCs), which we end functionalized with TAT (transactivator of transcription), an archetypal CPP built from a positively charged amino acid sequence of the HIV-1 virus. These ELPBCs self-assemble into micelles at a specific temperature and present the TAT peptide on their corona. These micelles can recover the lost membrane affinity of TAT and can trigger interactions with the membrane despite the presence of a molecular cargo. Herein, we study the influence of membrane surface charge on the adsorption of TAT-functionalized ELP micelles onto giant unilamellar vesicles (GUVs). We show that the TAT-ELPBC micelles show an increased binding constant toward negatively charged membranes compared to neutral membranes, but no translocation is observed. The affinity of the TAT-ELPBC micelles for the GUVs displays a stepwise dependence on the lipid charge of the GUV, which, to our knowledge, has not been reported previously for interactions between peptides and lipid membranes. By unveiling the key steps controlling the interaction of an archetypal CPP with lipid membranes, through regulation of the charge of the lipid bilayer, our results pave the way for a better design of delivery vectors based on CPPs.