The pressure-dependence of mechanical, electronic and thermodynamic properties of metastable (L12 type) and stable (D023 type) Al3Zr precipitations in Al-Li alloys were investigated by employing the first-principle calculations. The calculated equilibrium parameters are in good agreement with experimental and previous calculation results available. Elastic properties including bulk modulus, shear modulus, Young's modulus, Poisson's ratio and universal anisotropic index are determined by Voigt-Reuss-Hill approximation. It is found that for both phases, external pressure can improve the mechanical stability, ductility and plasticity. The electronic structures are determined to reveal the bonding characteristics of both phases. In addition, both phonon method and Gibbs program have been proposed to predict thermodynamic properties of two phases. All of these results can help to have a better understanding of the physical and chemical properties of Al3Zr precipitations in Al-Li alloy. And can offer theoretical guidance for the weight lighting, energy conservation and emissions reduction in the design of new aluminium alloys. [ABSTRACT FROM AUTHOR]