Diabetic patients are entangled to various cardiovascular diseases due to increased blood viscosity. Therefore the blood viscosity of diabetic patients is lowered by regular doses of Aspirin or the injection of saline water in order to dilute the blood. This lowers the blood pressure. In this model, the effect of non-Newtonian behaviour on blood flow through a stenosed artery using Casson’s fluid model have been studied and the results depict that the increase in blood flow characteristics are comparatively small due to the non-Newtonian behaviour of the blood. The numerical illustration presented at the end of this paper provides the results for the resistance to flow, apparent viscosity and the wall shear stress through their graphical representations. It has been shown that the resistance to flow, apparent viscosity and wall shear stress increases with the size of the stenosis but these increases are comparatively small due to the non-Newtonian behaviour of the blood indicating the usefulness of its rheological character in the functioning of diseased arterial circulation. A number of comparisons with the existing results have been made in order to validate the applicability of the present model.