Abstract: Receptor-mediated endocytosis is one of the means for cells to exchange materials with their environments. Vesicles coated with ligands on their surface are often adopted for the drug delivery in cancer therapy through receptor-mediated endocytosis as well. In the present work, we used a 3D mathematical model and energy minimization to study the endocytosis process of spherical drug nanoparticles. The total energy of the system including catch bonds was established. The minimization of the energy functional was carried out numerically. The shape of particle and cell membrane in each wrapping stage was obtained, and the influence of particle size on the minimum energy required for passive endocytosis was analysed. The results show that cell membrane and receptor-ligand bonds deformation energies are the major components of the total deformation energy, and each component changes as the wrapping area is increased. There exists an optimal size of nanoparticles for which the total energy consumption is minimum under given membrane stiffness and receptor-ligand bond strength. We also found that at the final stage of wrapping the endocytosis may not be completed because of the breaking of overstretched receptor-ligand bonds. This study provides a theoretical insight for the design of receptor mediated high efficiency drug delivery system.