Understanding the interactions of dendrimers as delivery vectors with biomembranes is important for functional optimization. Here, coarse-grained molecular dynamics simulations are employed to study the interactions between a surface-modified dendrimer with short peptides and lipid bilayers under physiological and low pH conditions. The peptide consists of three histidines (H) with the pH-sensitive property and an arginine (R). It is found that the peptide-dendrimer conjugate either adheres to or penetrates through the negatively charged, asymmetrical bilayer, dependent on the pH value. Calculation of the potential of mean force shows that the penetration is energy favorable at low pH. The conjugate can lead to membrane thinning with enhanced permeability. Inspired by the results, a possible route is proposed for gene delivery using the non-specific electrostatic interaction adjusted by the pH environment.