The study focuses on arterial stenoses in arteriovenous fistulae (AVF), the occurrence of which was long underestimated. The objective is to investigate their influence on the hemodynamic conditions within the AVF. A numerical simulation of the blood flow is conducted within a patient-specific arteriovenous fistula that presents an 60% stenosis on the inflow artery. In order to find the vessel shape without stenosis and compare the flow conditions with and without stenosis, the endovascular treatment of balloon-angioplasty is simulated by modeling the vessel deformation during balloon inflation implicitly. Clinically, balloon-angioplasty is considered successful if the post-treatment residual degree of stenosis is below 30%. Different balloon inflation pressures have been imposed numerically to obtain residual degrees of stenosis between 30 and 0%. The comparison of the computational fluid dynamic simulations carried out in the patient-specific native geometry and in the treated ones shows that the arterial stenosis has little impact on the blood flow distribution. The venous flow rate remains unchanged as long as thrombosis does not occur: the nominal flow rate needed for hemodialysis is maintained, which is not the case for a venous stenosis. An arterial stenosis, however, causes an increase in the pressure difference across the stenosed region. A residual degree of stenosis below 20% is needed to guarantee a pressure difference lower than 5 mmHg, which is considered to be the threshold stenosis pressure difference.