Arteriovenous fistula (AVF) is a vascular access and very import in hemodialysis that is a treatment for patients suffering from end-stage renal disease. Stenosis is considered the major cause of dysfunction of AVF. Despite the relatively low thrombosis rates of AVF, surveillance programs are necessary for detection of stenosis. However, conventional Doppler ultrasound cannot facilitate the risk assessment of AVF, such as insufficient resolution. The objective of this study was to develop an estimation system using FPGA based color relational analysis (CRA) method for AVF stenosis on hemodialysis patients by quantitative Doppler ultrasound, which provides not only the degrees of stenosis (DOS), but also anatomical locations and blood flow physiology information for clinical physicians, lowing the risk arising from treatment. In this paper we proposed a method based on hemodynamic analysis with dimensionless numbers to capture and further quantify the feature values of Doppler ultrasound extracted from intraluminal blood flow. The ratio of the supracritical Reynolds (Resupra) number and the resistive (Res) index were calculated via the peak-systolic and peak-diastolic velocities of blood flow from the arterial anastomosis sites (A) to the venous anastomosis sites (V) to quantitate the DOS at multiple measurement sites. After that, the results were mapped with a CRA classifier to real-time display the DOS. The examination results from thirty long-term dialysis patients showed that this proposed method performed well in DOS and occlusion site detection, with >95% of accuracy. This study confirmed the CRA method is a potential candidate method to effectively evaluate the AVF caused by long-term dialysis or vascular disease. The proposed system provides useful information with better accuracy and convenience for clinical examination.