Under the projector-augmented wave approach, the structural and thermodynamic properties of various intermetallic compounds in Mg–Zn–Cu alloys are investigated. The calculated results indicate that the intermetallic compounds Cu 0.7 Zn 2 , CuZn, Mg 4 Zn 8 , Mg 8 Cu 16 and Mg 8 Zn 8 Cu 8 are elastically stable at zero temperature and pressure. Cu 0.7 Zn 2 , CuZn Mg 4 Zn 8 and Mg 8 Cu 16 are the ductility phases, and Mg 8 Zn 8 Cu 8 is the brittleness phase. According to the calculations of the elastic constants and Young modulus, it is found that the plasticity of CuZn is the best while that of Mg 8 Zn 8 Cu 8 is the worst. Based on the quasi-harmonic Debye model, the vibrational internal energy, vibrational Helmholtz free energy, vibrational entropy, heat capacity of constant volume, heat capacity at constant pressure, thermal expansion coefficient, Grüneisen parameter and Debye temperature of the intermetallic compounds in Mg–Zn–Cu alloy under high pressure and high temperature are also deeply discussed.