First-principles calculations were performed to study on alloying stability, electronic structure, and mechanical properties of Al-based intermetallic compounds. The results show that the lattice parameters obtained after full relaxation of crystalline cells are consistent with experimental data. The calculation of cohesive energies indicated that the structure stability of these Al-based intermetallics will become higher with increasing Zr element in crystal. The calculations of formation energies showed that AlCu2Zr has the strongest alloying ability, followed by AlZr3 and finally the AlCu3. Further analysis finds out that single-crystal elastic constants at zero-pressure satisfy the requirement of mechanical stability for cubic crystals. The calculations on the ratio of bulk modulus to shear modulus reveal that AlCu2Zr can exhibit a good ductility, followed by AlCu3, whereas AlZr3 can have a poor ductility; however, for stiffness, these intermetallics show a converse order. The calculations on Poisson's ratio show that AlCu3 is much more anisotropic than the other two intermetallics. In addition, calculations on densities of states indicates that the valence bonds of these intermetallics are attributed to the valence electrons of Cu 3d states for AlCu3, Cu 3d and Zr 4d states for AlCu2Zr, and Al 3s, Zr 5s and 4d states for AlZr3, respectively; in particular, the electronic structure of the AlZr3 shows the strongest hybridization, leading to the worst ductility.