In this study, a finite element analysis based on a dislocation-based crystal plasticity model is performed to investigate a kink band formation and its evolution in an α-Mg/LPSO polycrystalline alloy. The present analysis model is composed of two α-Mg matrix phases and a LPSO phase, both having a rectangular shape, and tilt grain boundaries and a shape imperfection are introduced. The results show that a wedge-like deformation region formed on the free surface of the α-Mg phase propagates to the LPSO phase. In consequence, an arbitrary crystal lattice rotation is brought about locally and a kink band across the specimen is formed. In addition, the basal slips other than the predominant basal one and the non-basal slips are activated by stress concentration in the α-Mg phases around the phase interface in the kink band.