First principles calculations are performed to study structural， elastic and electronic properties of typical L12 precipitates of Al-based alloys （Al3Sc and Al3Zr）. The calculated formation energy and the cohesive energy show that both typical L12 precipitates of aluminum alloys have a strong alloying ability and Al3Zr phase has a higher structural stability than Al3Sc phase. According to the calculated density of states of these phases， it is found that the higher structural stability of Al3Zr is attributed to an increase in the number of bonding electrons below Fermi level. Three independent single-crystal elastic constants （C11，C12 and C44） at zero-pressure as well as polycrystalline mechanical parameters such as bulk modulus B， shear modulus G， Youngs modulus Y， Poissons ratio ν and anisotropy value A for both phases are calculated. The mechanical properties of both phases are further analyzed and discussed in comparison with experimental observations and other theory results.