This paper proposes a new automatic method for liver vessel segmentation by exploiting intensity and shape constraints of 3D vessels. The core of the proposed method is to apply two different strategies: 3D region growing facilitated by bi-Gaussian filter for thin vessel segmentation, and hybrid active contour model combined with K-means clustering for thick vessel segmentation. They are then integrated to generate final segmentation results. The proposed method is validated on abdominal computed tomography angiography (CTA) images, and obtains an average accuracy, sensitivity, specificity, Dice, Jaccard, and RMSD of 98.2%, 68.3%, 99.2%, 73.0%, 66.1%, and 2.56 mm, respectively. Experimental results show that our method is capable of segmenting complex liver vessels with more continuous and complete thin vessel details, and outperforms several existing 3D vessel segmentation algorithms.