Upon incubation of nanoparticles in biological uids, a new layer called as protein corona is formed on their surface affecting the interactions between nanoparticles and targeted cell during the endocytosis process. In the present study, a mathematical model based on the diffusion of membrane mobile receptors is proposed. Opposing the endocytosis proceeding, membrane bending and tension energies are named as resistant energy. Also, binding energy and free-energy associated with the congurational entropy are called as promoter energy. Utilizing this model, endocytosis of gold nanoparticle (GNP) is simulated to explore the biological media effect. The results reveal that there exists a nanoparticle size of 60nm at which, the endocytosis time is minimum. It has been illustrated that, although for sufficiently small particles of diameter 30nm, membrane tension has a negligible contribution (< 10%) in the resistant energy, it noticeably increases the endocytosis processing time for large particles. Therefore, we report several parametric studies to provide a better insight into the effects of biological media on the ingestion of nanoparticles. Through a detailed analysis of the engulfment of the nanoparticles, it is shown that the nanoparticle radius corresponding to the quickest possible ingestion time is affected in the presence of corona. Moreover, it is found that the formation of this layer can not only affect the endocytosis time but also can lead to incomplete engulfment by decreasing the ligand density on the nanoparticle surface. Use of the proposed model can play a signicant role in advancing the design of nanoparticles in the targeted drug delivery applications.