The Ciminio-Brescia arterio-venous fistula is a preferred vascular access for haemodialysis, but it is often associated with the development of vascular complications, due to changes in hemodynamic conditions. Computational fluid dynamics methods were involved to carry out seven simulations of the blood flow through the fistula for the patient specific (geometrical) case and various boundary conditions. The geometrical data, obtained from the angio-computed tomography, were used to create a 3-dimensional CAD model of the fistula. The blood flow patterns, blood velocity and the wall shear stress, thought to play a key role in the development of typical complications (stenoses, thromboses, aneurysms, etc.), have been analyzed in this study. The blood flow is reversed locally downstream the anastomosis (where the artery is connected to the vein) and downstream the stenosis in the cannulated vein. Blood velocity reaches abnormal value in the anastomosis during the systolic phase of the cardiac cycle (2.66 m/s). The wall shear stress changes in this place during a single cycle of the heart operation from 27.9 to 71.3 Pa (average 41.5 Pa). The results are compared with data found in the literature.