In this paper, we propose a novel vessel tracking method, called active vessel tracking (AVT). The proposed method retains the major advantages that most 2D segmentation methods have demonstrated for 3D tracking while overcoming the drawbacks of previous 3D vessel tracking methods. Under the assumption that the vessel is cylindrical, thereby making its cross-section elliptical, the AVT finds a plane perpendicular to the vessel axis while tracking the vessel along its length. Also, We propose a method for vessel branch detection to automatically track complete vascular networks from a single starting point, whereas the previously proposed solutions have usually been limited in handling vessel bifurcations precisely on 3D or have required considerable user interaction. Our results show that the method is robust and accurate in both synthetic and clinical cases. In an experiment on synthetic data sets, the proposed method achieved a tracking accuracy of 96.1±0.5, detecting 99.1% of the branches. In an experiment on abdominal CTA data sets, it achieved a tracking accuracy of 98.4±0.5 for six target vessels, detecting 98.3% of the branches. These results show that the proposed method can outperform previous methods for vessel tracking.