Since venous reflux is difficult to quantify, triggered angiography non-contrast-enhanced (TRANCE)-magnetic resonance imaging (MRI) is a novel tool for objectively evaluating venous diseases in the lower extremities without using contrast media. This study included 26 pre-intervention patients with superficial venous reflux in the lower extremities and 15 healthy volunteers. The quantitative flow (QFlow) analyzed the phase shift information from the pixels within the region of interest from MRI. The fast and simple radial basis function neural network (RBFNN) learning model is constructed by determining the parameters of the radial basis function and the weights of the neural network. The input parameters were the variables generated through QFlow, while the output variables were morbid limbs with venous reflux and normal limb classification. The stroke volume, forward flow volume, absolute stroke volume, mean flux, stroke distance, and mean velocity of greater saphenous veins from QFlow analysis could be used to discriminate the morbid limbs of pre-intervention patients and normal limbs of healthy controls. The neural network successfully classified the morbid and normal limbs with an accuracy of 90.24% in the training stage. The classification of venous reflux using the RBFNN model may assist physicians in clinical settings.