The influence of a heat-treatment on the plastic deformation behavior in Mg12ZnY with a long-period stacking ordered (LPSO) structure was investigated by using crystals grown by the Bridgman method. Annealing of the crystal at 798 K for 3 days induced the change in the crystal structure of Mg12ZnY from the 18-fold rhombohedral structure (18R) to the 14-fold hexagonal structure (14H). The plastic behavior of those LPSO crystals showed a large variation depending on the loading axis in both crystals, because of the limitation of operative deformation modes in them. The change in the stacking sequence in the LPSO crystals did not show a large influence on the plastic deformation behavior at room temperature.