Segmentation of ultrasound images is a challenging task due to the lower contrast and the speckle noise. Active contour is one of the most widely used techniques for ultrasound image segmentation. This method has drawbacks such as the predefined initial curve position and the number of contour points to be considered. A new active contour segmentation for extracting the intima media layer and plaque in the Common Carotid Artery (CCA) ultrasound images is presented in this paper. This paper has proposed a fuzzy weighted graph based active contour segmentation technique to overcome all these drawbacks. The proposed method is used for segmenting Intima-Media Thickness (IMT) and plaque in common carotid artery B-mode ultrasound images to assess the risk of stroke in the human subject under investigation. Using canny edge detection and connected component analysis methods, the initial contour was determined and applied as input to the proposed active contour segmentation algorithm. The proposed algorithm was compared with five conventional methods. Experimental results prove that the proposed approach has produced better results than traditional methods. The overall probability of error achieved by the proposed algorithm was 5.28%, which was very less compared to other conventional methods.