Ab initio calculation shows that the BCC NbHx (0 <= x <= 0.5) structure with H at tetrahedral(T) site is the most thermodynamically stable one among all the BCC, FCC, and HCP phases, and its negative heat of formation decreases linearly with the increase of H composition. Calculation also reveals that the elastic moduli of BCC(T) NbHx phases all increase with the increase of H composition, and the BCC(T) NbHx phases remain ductile within the studied composition range (0 <= x <= 0.5). Moreover, it is found that the percentage anisotropy in shear (A(G)) and the universal anisotropic parameter (A(U)) are all appropriate to describe the elastic anisotropy of NbH phases, and that H location should play an important role in elastic anisotropy. The fundamental mechanism of various properties is deeply understood by means of electronic structures, and the present results agree well with experimental investigations in the literature. Copyright (C) 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.