Nanoparticles have been widely used in biomedical applications such as gene/drug delivery, molecular imaging and diagnostics. Among the physicochemical properties, shape is a vital design parameter for tuning the cell uptake of nanoparticles. However, the regulatory mechanism remains elusive due to the complexity of the cell membrane and multiple pathways of cell uptake. Therefore, in this computational study, we design and clarify cell membrane wrapping on different shaped nanoparticles (sphere, rod and disk) with a clathrin assembly to model the clathrin-mediated endocytosis, which is an important pathway of nanoparticle cell uptake. Our simulations revealed that the clathrin-mediated endocytosis is shape sensitive for nanoparticles. Spherical nanoparticles are easier to be wrapped by the membrane with the self-assembly of clathrins than the other shaped nanoparticles with the same volume, and the efficiency declines with the increase in the nanoparticle shape anisotropy. Furthermore, simulation results showed clear evidence that rotation is one of the typical characteristics determining the kinetics of clathrin-mediated endocytosis of shaped nanoparticles. Especially for rod nanoparticles with high aspect ratios, nanoparticle rotation occurs in both the invagination and wrapping stages, which is different from the case without clathrins. The size and shape mismatch between the clathrin-mediated vesicle and the nanoparticle determines how the nanoparticle rotates and is wrapped by the membrane. In addition, the wrapping time of nanoparticles depends not only on the shape of the nanoparticle but also on its initial orientation and size, the rate of clathrin self-assembly and the surface tension of the membrane. These results provide insights into the interplay between cell membrane wrapping and clathrin assembly, where the nanoparticle shape matters. Understanding the dynamics mechanism of clathrin-mediated endocytosis of nanoparticles will help to design targeted nanomedicines with an improved efficacy.