Deformation behaviors of the LPSO and α-Mg phases in the microstructure of a high-strength Mg alloy of LPSO type were studied by a crystal plasticity software code. Results showed that in the LPSO phase , large stress was generated and accumulation of GN dislocation corresponding to kink deformation was observed. In α-Mg phase, deformation was highly nonuniform due to the anisotropy of the HCP structure, but kink deformation did not occur.