We report atomic-scale observations on the interaction of {101ˉ2} deformation twins with 14H long-period stacking ordered (LPSO) phase in a magnesium alloy. It was found that the interaction strongly depends on the thicknesses of LPSO plates as well as the thickness ratios between LPSO plates and twins. We observed three size-dependent structure responses of LPSO to incoming twins: (1) pure shearing of thin LPSO plates in line with the incursive {101ˉ2} twins; (2) twin-to-dislocation ‘switch’ from the alpha-Mg matrix to LPSO when LPSO/twin thickness ratios are below a critical value of 0.17 ± 0.01; and (3) elastic deformation of LPSO to accommodate the propagation of incoming twin when LPSO/twin thickness ratios are larger than 0.17 ± 0.01. Moreover, the inter-plate spacing of LPSO also influences the propagation modes of twins by controlling nucleation sites of new twins. These size-dependent interactions are accomplished by local structural transition of face-centered cubic units of LPSO during thin plate shearing and formation of gliding dislocations during LPSO deformation and twin blocked. The atomic-scale observations provide fundamental insights into these interaction modes and, hence, the precipitation strengthening mechanisms in Mg alloys under both quasi-static and dynamic loadings.