We have predicted structural, electronic, elastic, thermodynamic and vibration characteristics of TbN, using density functional theory within generalized-gradient (GGA) apraximation. For the total energy calculation we have used the projected augmented plane-wave (PAW) implementation of the Vienna Ab initio Simulation Package (VASP). We have used to examine structure parameter in eight different structures such as in NaCl (B1), CsCl (B2), ZB (B3), Tetragonal (L1(0)), WC (Bh), NiAs (B8), PbO (B10) and Wurtzite (B4). We have performed the thermodynamics properties for TbN by using quasi-harmonic Debye model. We have, also, predicted the temperature and pressure variation of the volume, bulk modulus, thermal expansion coefficient, heat capacities and Debye temperatures in a wide pressure (0-130 GPa) and temperature ranges (0-2000 K). Furthermore, the band structure, phonon dispersion curves and corresponding density of states are computed. Our results are compared to other theoretical and experimental works, and excellent agreement is obtained. (C) 2012 Elsevier Masson SAS. All rights reserved.