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The crystal structure of the single-unit-cell thickness γ″ phase, as a key strengthening phase in Mg-RE-Zn (Ag) series alloys, has been extensively studied, and several structural models have been proposed in the past two decades. However, these reported models, and even the lattice constants at the same proposed structure, are scattered severely, which has led to considerable confusion and not available for further mechanical property simulation and prediction of Mg alloys containing this phase. In this study, by using first-principles calculations, the crystal structure of γ" phase is clarified, resolving the discrepancies among different experiments, and its intrinsic mechanical properties have also been studied for the first time. It is verified that the γ″ phase contains quasi-five atomic layers, instead of the previously reported tri-layer, and surprisingly, its crystal structure has many variants, which would change with the alloy composition. Besides, with the help of the simulated selected area electron diffraction (SAED) patterns, it is found that the atoms in the central layer remain partially ordered distribution, and this ordered extent primarily depends on the atomic ratio of RE: Zn(Ag) and the solute content in an alloy. That is, the ordered extent increases with decreasing the atomic ratio of RE:Zn(Ag) and/or increasing solute content of alloy, and vice versa. Ag and Zn dissolved in the γ″ phase would produce almost opposed mechanical anisotropy for the γ″ phase under the identical crystal structure, and the addition of Ag shows more efficient on increasing the shear modulus of γ″ phase. [ABSTRACT FROM AUTHOR]