The crystal structures of highly-ordered Mg-Zn-Y long-period stacking-ordered (LPSO) phases with the 18R, 14H and 10H-type stacking sequences have been investigated by atomic-resolution scanning transmission electron microscopy (STEM) and transmission electron microscopy (Kishida et al., 2015) [1]. This data article provides supporting materials for the crystal structure analysis based on the crystallographic theory of the order-disorder (OD) structure and the crystallographic information obtained through the structural optimization for various simple polytypes of the highly-ordered Mg-Zn-Y LPSO phases with the 18R, 14H and 10H-type stacking sequences by first-principles density functional theory (DFT) calculations.