In this research a two dimensional, single phase, and isothermal model is developed to investigate the effects of eccentric catheterization on blood flow characteristics in a tapered and stenosis artery which is complex system. The model conducted by assuming that the blood is as Newtonian and incompressible fluid and the temperature effects are also neglected. The results clearly show that the axial velocity and the magnitude of the wall shear stress distribution are higher for eccentric catheter than that for concentric one. Also, the resistance impedance gives the reverse trend of the wall shear stress with respect to the taper angle where blood can flow freely through diverging vessel but in the case of eccentric catheter is less than that of the concentric one when the radius of catheter is considered. In addition, the trapping appears near the wall of catheter and the trapped bolus increases in size as the radius of catheter increases.