First principles calculations have been carried out to investigate the electronic structure and the mechanical properties of α-Mg3Sb2. The optimized structural parameters and formation energy are in good agreement with the experimental values. The electronic structure is also given， indicating that α-Mg3Sb2 is indirect-semiconductor. The obtained energy band gap of α-Mg3Sb2 is 0.303 eV. The elastic constaint Cij of α-Mg3Sb2 has been calculated，then the mechanical parameters such as moduli, Possions ratio, etc are abtained. By analysizing the mechanical parameters it is found that α-Mg3Sb2 has good ductility and relatively poor plasticity. In the end，the volume conservation of α-Mg3Sb2 is discussed in terms of the total density of states before and after deformations. From the results， it can be seen that the shears corresponding to （C11-C12）/4 and C44 are almost volume conserving whereas the shears corresponding to C11+C12，C33/2 and the bulk modulus related to C11+C12+2C13+C33/2 are not volume conserving.