Quantitative coronary arteriography (QCA), a method to detect and quantify coronary arteries, is important to prevent misinterpretation of arteriograms. We propose a hierarchical neural network QCA system. The system uses classical supervised feedforward networks using backpropagation learning with an unfair weight update technique. The learning process is slow but does not impede the quantifying process because it is done off-line. The hierarchical structure works for: fast detection of the location of the artery; fast computation of the orientation; taking into account of the intensity ratio between stenotic lesion and the normal part of the artery; and dimension reduction (two dimensional to one dimensional signal processing).