Metallic glasses have been established to have unique properties such as ductility, toughness, and soft magnetism with promising engineering applications. However, the glass-forming ability (GFA) has not been sufficient to synthesize the bulk metallic glasses (BMGs) required for many engineering applications. Attempts to develop the understanding of the GFA required to predict the optimum alloys have not yet been proven successful. We develop here a computational model based on molecular dynamics simulations that explains the dramatic change of GFA with alloying small amounts of Al into Cu-Zr. We find that the high GFA to form BMGs depends on a combination of three factors, (a) a low thermodynamic driving force for crystallization, (b) a high melt viscosity, and (c) large ratios of icosahedral structures in the liquid phase. These computational methods to predict these factors that suppress formation of crystal nuclei and slow the dynamic motions in the liquids are practical for in silico prediction of new alloys with optimal GFA.