The ground-state lattice constants, bulk modulus and six independent elastic constants of β-Si3N4 have been calculated through the framework of density functional theory within the plane-wave pseudopotential method. The quasi-harmonic Debye model, by means of total energy versus volume calculations obtained with the plane-wave pseudo-potential method, is applied to the study of the thermal, elastic and vibrational effects. In the temperature interval 0--1800K, the calculated results agree reasonably with numerous experimental and theoretical data. Other thermal outcomes gained from this method provide overall predictions accurately for the temperature and pressure dependence of different quantities such as the thermal expansion, heat capacity and Debye temperature. The variations of Debye temperature ӨD with temperature are analysed, which show the temperature has hardly any effect on ӨD. Therefore, the present study indicates that first-principles combined with quasi-harmonic Debye model is an effective way to stimulate the behaviors of solids at simultaneously high temperature and pressure.