Based on the first-principles density functional theory calculations combined with the quasi-harmonic Debye model, the ground state structure, equation of state (EOS), elastic and thermal properties of YbB6 crystal are studied. The calculated results of the lattice constant, bulk modulus and elastic constants in YbB6 crystal are in good agreement with the experimental results. The research results of EOS show that the effects of pressure and temperature on the volume of YbB6 crystal are very significant, and the pressure has more influence on the volume of the YbB6 crystal under higher temperatures and lower pressures than that of case under the lower temperatures and lower pressures. Furthermore, the bulk modulus is greatly affected by the pressure compared with the temperature in the whole pressure and temperature ranges. The results of elastic constants and elasticity-relevant properties show that the YbB6 crystal is mechanically stable with a ductile manner and is solid with a central force field under zero temperature and 0 GPa pressure. The calculated values of the heat capacity and thermal expansion coefficient indicate that the influence of pressure on the heat capacity and expansion coefficient of YbB6 crystal is less than that of temperature.