Nano-sized precipitates in Al-Mg-Si alloys can effectively increase the mechanical property of these alloys. However, nanoscale dimensions and orientation variations greatly impede the understanding of crystal structures and phase relations of precipitates. In this paper, the structural stability, mechanical, and electronic properties of twelve Al-Mg-Si compounds in Al-Mg-Si alloys are examined systematically using first-principles calculations. The calculated results of Mg2Si and MgAlSi agree well with the previous experimental and theoretical results. The Mg4Si7 with P (1) over bar symmetry, MgAl2Si2 with C2/m symmetry, and Mg4AlSi3 with Pccn symmetry are identified as the more energetically and mechanically favorable phases suggested by our calculations. According to the predictions, MgSi2 and MgAlSi exhibit higher bulk moduli, 73.1 and 67.7 GPa, due to the tightly bounding Si-Si/Si-Al covalent networks.