We propose an anatomy-based approach for an efficient construction of a three-dimensional human normal cerebral arterial model from segmented and skeletonized angiographic data. The centerline-based model is used for an accurate angiographic data representation. A vascular tree is represented by tubular segments and bifurcations whose construction takes into account vascular anatomy. A bifurcation is defined quantitatively and the algorithm calculating it is given. The centerline is smoothed by means of a sliding average filter. As the vessel radius is sensitive to quality of data as well as accuracy of segmentation and skeletonization, radius outlier removal and radius regression algorithms are formulated and applied. In this way, the approach compensates for some inaccuracies introduced during segmentation and skeletonization. To create the frame of vasculature, we use two different topologies: tubular and B-subdivision based. We also propose a technique to prevent vessel twisting. The analysis of the vascular model is done on a variety of data containing 258 vascular segments and 131 bifurcations. Our approach gives acceptable results from anatomical, topological and geometrical standpoints as well as provides fast visualization and manipulation of the model. The approach is applicable for building a reference cerebrovascular atlas, developing applications for simulation and planning of interventional radiology procedures and vascular surgery, and in education.