The long-period stacking-ordered (LPSO) phases were demonstrated to be the predominant strengthening phases that can significantly improve the mechanical properties of Mg-Zn-Y alloys. However, the mechanism underlying this improvement has not been satisfyingly understood yet due to unclear characterization of the microstructures of these LPSO phases. We proposed the reliable structural model of Mg142Zn12Y16 for 14H LPSO phase formed in Mg-Zn-Y alloys with first-principles calculations in this study. The space group of Mg142Zn12Y16 is P6(3)/mcm, with lattice dimensions a = b = 11.168 angstrom, c = 36.408 angstrom, alpha = beta = 90 degrees, and gamma = 120 degrees. And the atomic sites were given in this work. In contrast to other structural models proposed in previous studies, 14H LPSO phase was predicted to be thermodynamically stable on the basis of the present structural model, which can well account for the stability of 14H LPSO phases at higher temperature. Furthermore, the elastic constants and elastic moduli of 14H LPSO phase were also evaluated based on the present structural model. The calculated Young's modulus of 14H LPSO phase agrees well with the available experimental values. The characteristics of 14H LPSO phase observed in experiments were successfully reproduced using the present structural model. The good match between the calculations and the experiments validates the reliability of the structural model proposed for 14H LPSO phase.