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The first-principles calculation based on density functional theory has been carried out to study the microstructural feature of the novel 24R-type long period stacking ordered structure in Mg97Zn1Y2 alloy. The lattice positions of the Y and Zn atoms are determined theoretically, it is shown that the additive atoms are firstly enriched in the stacking fault layers at the two ends, a small amount are distributed in the interior stacking fault layers of the structure. And 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 as.