The mechanical, electronic and elastic properties of Mo2XB2 (X = Nb, Os, Ta) at different pressures (0-50 GPa) were predicted using first-principles calculations. The enthalpy of formation and the elastic constant calculations show that the three transition metal borides are thermodynamically and mechanically stable. The analysis of density of state and band structure reveals that Mo2XB2 (X = Nb, Os, Ta) have metallic and covalent properties. The increase of pressure will increase the elastic modulus of Mo2XB2 (X = Nb, Os, Ta). The elastic modulus of Mo2XB2 (X = Nb, Os, Ta) are anisotropic. Furthermore, the quasi-harmonic Debye model is used to predict thermodynamic parameters at various temperatures (0-1200K) and pressures (0-50 GPa), such as heat capacity at constant pressure, heat capacity at constant volume, coefficient of thermal expansion, Debye temperature, and the Gr & uuml;neisen parameter.