The structural, elastic, thermodynamic, electronic and vibrational properties of CsCI-type TbMg have been studied by performing ab initio calculations based on density functional theory using the Vienna Ab initio Simulation Package (VASP). The exchange correlation potential within the generalized-gradient approximation (GGA) of projector augmented wave (PAW) method is used. The calculated structural parameters, such as the lattice constant, bulk modulus, its pressure derivative, formation energy and second-order elastic constants are presented in this paper. The obtained results are compared with related experimental and theoretical studies. The electronic band calculations, total density of states (DOS), partial DOS and charge density are also presented. Formation enthalpy and Cauchy pressure are determined. In order to obtain more information the elastic properties such as Zener anisotropy factor, Poisson's ratio, Young modulus, isotropic shear modulus, Debye temperature and melting point have been carried out. The elastic constants are calculated in zero and different pressure ranges (0-50 GPa) with bulk modulus. We have performed the thermodynamic properties of TbMg by using quasi-harmonic Debye model. The temperature and pressure variation of the volume, bulk modulus, and thermal expansion coefficient have been predicted over a pressure range of 0-25 GPa for of TbMg. Pressure dependence of the anisotropy factors, Young's modulus, Poisson's ratios, bulk modulus and axis compressibility of TbMg are presented along different directions and planes. Finally, the phonon dispersion curves are presented for TbMg. (C) 2014 Elsevier Ltd. All rights reserved.