The lattice constants, elastic properties, electronic structure and thermodynamic properties of Al 3 Nb with DO 22 structure have been investigated by the first-principles calculation. The calculated lattice constants were consistent with the experimental values, and the structural stability was also studied from the energetic point of view. The single-crystal elastic constants (C ij ) as well as polycrystalline elastic parameters (bulk modulus B, shear modulus G, Young's modulus E, Poisson's ratio υ and anisotropy value A) were calculated, and brittleness of Al 3 Nb was discussed in detail. Besides, the electronic structure of tetragonal Al 3 Nb was studied, which indicates a mixture of metallic bond and covalent bond in Al 3 Nb and reveals the underlying mechanism of the stability and elastic properties of Al 3 Nb. Finally, the thermodynamic properties of Al 3 Nb were calculated and the physical properties such as heat capacity and Debye temperature were predicted within the quasi-harmonic approximation.