A set of atomic polarizability parameters for a new polarizable Gaussian model (pGM) has been developed with the goal to accurately reproduce the polarizability anisotropy, taking advantage of its ability to attenuate all short-range electrostatic interactions, by fitting the ab initio molecular polarizability tensors (A pq) calculated at the B3LYP/aug-cc-pVTZ level. For comparison, we also rederived the parameters for three Thole models in which the 1-2 (bonded), 1-3 (separated by two bonds) and 1-4 (separated by three bonds) interactions are fully included. The average percent errors (APEs) of molecular polarizability tensors for 4842 molecules or dimers are 2.98, 3.76, 3.28, and 3.82% for the pGM, Thole linear, Thole exponential, and Thole Amoeba models, respectively, with atom-type independent, universal screening factors (USF). The APEs are reduced further to 2.30, 2.69, 2.25, and 2.48% for the four corresponding polarizable models with atom-type dependent, variable screening factors (VSF). It is encouraging that the pGM with variable screening factors achieved APEs of 1.83 for 1155 amino acid analogs, dipeptides and tetrapeptides, 1.39 for 28 nucleic acid bases, 0.708 for 1464 water clusters, and 1.99 for 85 dimers of water and biological building blocks. Compared to the new set of models, the APEs of the old Thole models that were fitted to isotropic molecular polarizabilities are 8.7% for the Set A (without the 1-2 and 1-3 interactions) and 6.3% for the Set D (with the 1-2 and 1-3 interactions) models, respectively. MPAD, a metric of molecular polarization anisotropy difference based on the diagonal terms of molecular polarizability tensors was defined and applied to assess