The blood-brain barrier (BBB) is a highly specialised compartment surrounding the brain that includes layers of endothelial cells (ECs), pericytes, basement membrane, and astrocytes. BBB tightly regulates the traverse of materials toward brain cells and hence, strongly prevents the entrance of most therapeutics into the brain. This has become a considerable rate-limiting factor in drug delivery to the brain and brain tumours and has significantly reduced the survival of patients with metastatic brain lesions or brain tumours to <2 years. To increase drug delivery across BBB and improve the patient’s outcome, we developed aptamers targeting transferrin receptors on BBB ECs and showed increased drug delivery to the brain. To improve the understanding of aptamer delivery across BBB, we developed a mathematical model based on the finite element method across a 14 µm neovascular unit (NVU) representing a section of BBB. The model described the fluid flow and aptamer transport inside an 8 µm-capillary vessel. Coupled fluid flow and mass transport equations were solved to calculate the aptamer concentration (Capt) profiles and spatial blood velocity across the NVU, with a blood velocity of 0.38 mm/s, which was independent of the inlet Capt. The results demonstrated the key parameters affecting the Capt delivered to the neurons to be the thickness of the ECs and astrocytes. The results showed a low aptamer delivery of ~11% and ~14% at porosities of 0.5 and 0.9, which was attributed to the mass transfer resistance across the cell layers, and caused a 7% decrease in Capt. In addition, the main transport mechanism of aptamer delivery in the capillary was convective mass transport which switched to mixed convection mass transport in the cell layers and to pure diffusion in the brain parenchyma. The results also showed that higher blood pressures decreased aptamer delivery to the brain. The model developed in this study can be used for additional dose optimisation and adjustment studies for aptamer delivery to brain tumours.