The long-period stacking-ordered (LPSO) phase discovered in magnesium alloys is deformed upon the generation of a large number of unique deformation zones, which have no distinct orientation relationships at the deformation boundaries. These deformation zones are considered kink bands, but the mechanisms underlying their generation are not well understood. It has been suggested that the kink bands are responsible for the deformation of the LPSO phase, while simultaneously strengthening the material. In this study, the kink deformation process of the LPSO phase under compressive deformation was investigated through molecular dynamics (MD) simulations. The MD simulations showed that numerous prismatic ⟨a⟩ dislocations were nucleated first, which led to cross-slips towards various basal planes and caused kink deformation. This was followed by the nucleation and motion of a large number of basal dislocations, as well as kink deformations in tandem with the formation of kink bands, which occurred through another process. In addition, the individual dislocations were indistinguishable at kink boundaries. In other words, sharp boundaries were formed. Next, a simulation was performed that applied tensile strain to the model after the compressive deformation described above was implemented on it. This revealed that while kink boundaries with large misorientation angles intermittently migrated because of the tensile strain, the kink bands were not easily removed.