Abstract: Sufficient blood supply is of importance in maintaining the normal function of brain. If the brain cells are lack of oxygen for more than a few minutes due to decreased flow and perfusion pressure, they will be irreversibly damaged. In this study, blood flow and oxygen transport in the circle of Willis are modeled using one-dimensional equations derived from the axisymmetric Navier-Stokes equations for flow in elastic and compliant vessels and the convective-diffusive equation with the consideration of the diffusion from the lumen to artery wall and the metabolism produced by the wall cells. The nonlinear equations for hemodynamics were numerically solved using the two-step Lax-Wendroff scheme, and the upwind scheme was used in the discretization of the oxygen transport equations. The computational results were obtained, which were in good agreement with the available physiological data in normal and stenosis condition. It is shown that, when the degree of stenosis existing at the right internal carotid artery is up to 80%, the flow rate of the middle cerebral artery is reduced significantly. Furthermore, the oxygen partial pressure in ipsilateral vessels decreases with the increasing of stenosis degree, while the oxygen partial pressure of the vessel in another side increases.