The equilibrium lattice parameter, relative volume V/Vo, elastic constants Cij, and bulk modulus of titanium nitride are successfully obtained using the ab initio plane-wave pseudopotential (PW-PP) method within the framework of density functional theory. The quasi-harmonic Debye model, using a set of total energy vs molar volume obtained with the PW-PP method, is applied to the study of the elastic properties and vibrational effects. We analyze the relationship between the bulk modulus and temperature up to 2000 K and obtain the relationship between bulk modulus B and pressure at different temperatures. It is found that the bulk modulus B increases monotonously with increasing pressure and decreases with increasing temperature. Moreover, the Debye temperature is determined from the non-equilibrium Gibbs func-tions.