The structural, elastic and electronic properties of Al 2 La, AlLa 3 and Al 3 La binary intermetallics in the Al–La alloy system were investigated using the first-principles method. The calculated lattice constants were consistent with the experimental values. Formation enthalpy and cohesive energy showed that the studied Al 2 La, AlLa 3 and Al 3 La all have a higher structural stability, and the alloying ability of Al 2 La and Al 3 La is stronger than that of AlLa 3 . 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 by the Voigt–Reuss–Hill (V–R–H) approximations, and the relationship of these elastic parameters between Al 2 La, AlLa 3 and Al 3 La phases were discussed in detail. The results showed that Al 2 La and Al 3 La which are anisotropic materials are absolutely brittle, while the isotropic AlLa 3 is slightly ductile. Finally, the electronic density of states (DOS) was also calculated to reveal the underlying mechanism of structural stability.