An interatomic potential is constructed for the ternary Al-Mg-Zn system under a proposed modified tight-binding scheme, and it is verified to be realistic. Applying this ternary potential, atomistic simulations predict an intrinsic glass formation region in the composition triangle, within which the glassy alloys are more energetically favored in comparison with their solid solution counterparts. Kinetically, the amorphization driving force of each disordered state is derived to correlate the readiness of its glass-forming ability in practice; thus, an optimal stoichiometry region is pinpointed around Al35Mg35Zn30. Furthermore, by monitoring the structural evolution for various (Al50Mg50)1−xZnx (x = 30, 50, and 70 at.%) compositions, the optimized-glass-former Al35Mg35Zn30 is characterized by both the highest degree of icosahedral ordering and the highest phase stability among the investigated compositions. In addition, the icosahedral network in Al35Mg35Zn30 exhibits a much higher cross-linking degree than that in Al25Mg25Zn50. This suggests that there is a certain correlation between the icosahedral ordering and the larger glass-forming ability of Al35Mg35Zn30. Our results have significant implications in clarifying glass formation and hierarchical atomic structures, and in designing new ternary Al-Mg-Zn glassy alloys with high GFA.