In this paper, we present a novel technique for automatic parametric mesh generation of subject-specific cerebral arterial trees. This technique generates high-quality and anatomically accurate computational meshes for fast blood flow simulations extending the scope of 3D vascular modeling to a large portion of cerebral arterial trees. For this purpose, a parametric meshing procedure was developed to automatically decompose the vascular skeleton, extract geometric features and generate hexahedral meshes using a body-fitted coordinate system that optimally follows the vascular network topology. To validate the anatomical accuracy of the reconstructed vasculature, we performed statistical analysis to quantify the alignment between parametric meshes and raw vascular images using receiver operating characteristic curve. Geometric accuracy evaluation showed an agreement with area under the curves value of 0.87 between the constructed mesh and raw MRA data sets. Parametric meshing yielded on-average, 36.6% and 21.7% orthogonal and equiangular skew quality improvement over the unstructured tetrahedral meshes. The parametric meshing and processing pipeline constitutes an automated technique to reconstruct and simulate blood flow throughout a large portion of the cerebral arterial tree down to the level of pial vessels. This study is the first step towards fast large-scale subject-specific hemodynamic analysis for clinical applications.