The scope of this paper is to present a new carotid vessel segmentation algorithm implementing the U-net based convolutional neural network architecture. With carotid atherosclerosis being the major cause of stroke in Europe, new methods that can provide more accurate image segmentation of the carotid arterial tree and plaque tissue can help improve early diagnosis, prevention and treatment of carotid disease. Herein, we present a novel methodology combining the U-net model and morphological active contours in an iterative framework that accurately segments the carotid lumen and outer wall. The method automatically produces a 3D meshed model of the carotid bifurcation and smaller branches, using multispectral MR image series obtained from two clinical centres of the TAXINOMISIS study. As indicated by a validation study, the algorithm succeeds high accuracy (99.1% for lumen area and 92.6% for the perimeter) for lumen segmentation. The proposed algorithm will be used in the TAXINOMISIS study to obtain more accurate 3D vessel models for improved computational fluid dynamics simulations and the development of models of atherosclerotic plaque progression.