A three-dimensional compression analysis is performed by finite element method using a dislocation-based crystal plasticity model to clarify the formation mechanism of kink band in a polycrystalline Mg alloy with a long-period stacking ordered structure (LPSO) phase. The crystalline structure of LPSO phase is regarded as a HCP for simplicity, however, any deformation twinning is not taken into account. In addition, the activities of non-basal systems are considerably limited in the LPSO phase setting the values of their critical resolved shear stresses to large ones. We analyze a simple polycrystalline specimen composed of two α-Mg matrix phases and a LPSO phase both having a rectangular shape and twist grain boundaries are introduced into the interface. The obtained result shows that the kink band formation in the alloy is accomplished by the basal slips with different variants and the non-basal slips are activated on the grain boundary to maintain the continuity of deformation.