The mechanical properties of the Mg-based LPSO-phase are expected to be strongly affected by the microstructure due to its anisotropic crystal structure. However, the fine details have not been sufficiently understood yet. This study first clarified the detailed microstructural factors that govern the strength of the LPSO-phase by examining alloys with microstructures that were significantly varied via directional solidification and extrusion processes. Refining the microstructure is significantly effective for strengthening LPSO-phase alloys. The yield stress of LPSO-phase alloys with random texture was previously reported to be increased by reducing the “length” of plate-like LPSO-phase grains. In addition, it was found in this study that the formation stress in the deformation kink band, which is a unique deformation mode in an LPSO-phase alloy, can be increased by decreasing the “thickness” of the grains. Furthermore, the study used directionally solidified crystals provided direct evidence that the introduction of the deformation kink band effectively increases the yield stress and work-hardening rate of alloys by hindering the motion of basal dislocations. This “kink-band strengthening” was found to have considerable temperature dependence. The strengthening is significant at or below 200 °C, but the effect gradually decreases above 300 °C and is accompanied by the operation of non-basal slip. The results quantitatively clarified that kink-band strengthening is one predominant reason why the LPSO-phase extruded alloy exhibits an unusually high yield stress at any loading orientation.