Wrapping dendrimer-like soft nanoparticles by cell membrane is an essential event in their endocytosis in drug and gene delivery, but this process remains poorly elucidated. Using computer simulations and theoretical analysis, we report the detailed dynamics of the process in which a lipid bilayer membrane fully wraps a dendrimer-like soft nanoparticle. By constructing a phase diagram, we firstly demonstrate that there exist three states in the interaction between a dendrimer and a lipid bilayer membrane, i.e., penetration, penetration and partial wrapping, and full wrapping states. The wrapping process of dendrimer-like nanoparticles is found to take a unique approach where the penetration of the dendrimer into the membrane plays a significant role. The analysis of various energies within the system provides a theoretical justification to the state transition observed from simulations. The findings also support recent experimental results and provide a theoretical explanation for them. We expect that these findings are of immediate interest to the study of the cellular uptake of dendrimer-like soft nanoparticles and can prompt the further application of this class of nanoparticles in nanomedicine.