Arginine-rich cell-penetrating peptides (RRCPPs) exhibit intrinsic neuroprotective effects on neurons injured by acute ischemic stroke. Conformational properties, interaction, and the ability to penetrate the neural membrane are critical for the neuroprotective effects of RRCCPs. In this study, we applied circular dichroism (CD) spectroscopy and coarse-grained molecular dynamics (CG MD) simulations to investigate the interactions of two RRCPPs, Tat(49-57)-NH (arginine-rich motif of Tat HIV-1 protein) and PTD4 (a less basic Ala-scan analog of the Tat peptide), with an artificial neuronal membrane (ANM). CD spectra showed that in an aqueous environment, such as phosphate-buffered saline, the peptides mostly adopted a random coil (PTD4) or a polyproline type II helical (Tat(49-57)-NH) conformation. On the other hand, in the hydrophobic environment of the ANM liposomes, the peptides showed moderate conformational changes, especially around 200 nm, as indicated by CD curves. The changes induced by the liposomes were slightly more significant in the PTD4 peptide. However, the nature of the conformational changes could not be clearly defined. CG MD simulations showed that the peptides are quickly attracted to the neuronal lipid bilayer and bind preferentially to monosialotetrahexosylganglioside (DPG1) molecules. However, the peptides did not penetrate the membrane even at increasing concentrations. This suggests that the energy barrier required to break the strong peptide-lipid electrostatic interactions was not exceeded in the simulated models. The obtained results show a correlation between the potential of mean force parameter and a peptide's cell membrane-penetrating ability and neuroprotective properties.