Doppler ultrasound is an important noninvasive diagnostic tool for cardiovascular diseases. Modern ultrasound imaging systems utilize spectral Doppler techniques for quantitative evaluation of blood flow velocities, and these measurements play a crucial rule in the diagnosis and grading of arterial stenosis. One drawback of Doppler-based blood flow quantification is that the operator has to manually specify the angle between the Doppler ultrasound beam and the vessel orientation, which is called the Doppler angle, in order to calculate flow velocities. In this paper, we will describe a computer vision approach to automate the Doppler angle estimation. Our approach starts with the segmentation of blood vessels in ultrasound color Doppler images. The segmentation step is followed by an estimation technique for the Doppler angle based on a skeleton representation of the segmented vessel. We conducted preliminary clinical experiments to evaluate the agreement between the expert operator's angle specification and the new automated method. Statistical regression analysis showed strong agreement between the manual and automated methods. We hypothesize that the automation of the Doppler angle will enhance the workflow of the ultrasound Doppler exam and achieve more standardized clinical outcome.