The microstructural feature of the long period stacking ordered (LPSO) structure in Mg-Y-Zn alloy has been systematically studied based on the density functional theory. The lattice positions of the Y and Zn atoms had been studied theoretically. It is shown that the additive atoms are firstly enriched in the stacking fault layers at the two ends, and a small amount are distributed in the interior stacking fault layers of the structure. The arrangement of these Y and Zn atoms trends to be along the diagonal line of the unit cell. The structural stability is analyzed, and the electronic density of state is discussed as well.