For patients with renal failure, renal replacement therapies are needed. Hemodialysis is a widely used renal replacement method to remove waste products. It is important to improve the patency rate of the vascular access for efficient dialysis. Since some complications such as an intimal hyperplasia are associated with the flow pattern, the hemodynamics in the vascular access must be considered to achieve a high patency rate. In addition, the blood flow from an artificial kidney affects the flow in the vascular access. Generally, the clinical techniques of hemodialysis such as the catheter angle or dialysis dose have been set up empirically. In this study, a numerical analysis is performed on the effect of the catheter angle on the flow in the graft. Blood is assumed to be a non-Newtonian fluid. According to the high average wall shear stress value, the leucocytes and platelets can be activated not only at the arterial anastomosis, but also at the bottom of the venous graft, when the catheter angle is not zero. For a catheter angle less than five degrees, there is a low shear and high oscillatory shear index region that appears at the venous graft and the venous anastomosis. Thus, a catheter angle less than five degrees should be avoided to prevent graft failure.