Glass is a freezing phase of a deeply supercooled liquid. Despite its simple definition, the origin of glass forming ability (GFA) is still ambiguous, even for binary Cu-Zr alloys. Here, we directly study the stability of the supercooled Cu-Zr liquids where we find that Cu64Zr36 at a supercooled temperature shows deeper undercoolability and longer persistence than other neighbouring compositions with an equivalent driving Gibbs free energy. This observation implies that the GFA of the Cu-Zr alloys is significantly affected by crystal-liquid interfacial free energy. In particular, the crystal-liquid interfacial free energy of Cu64Zr36 in our measurement was higher than that of other neighbouring liquids and, coincidently a molecular dynamics simulation reveals a larger glass-glass interfacial energy value at this composition, which reflects more distinct configuration difference between liquid and crystal phase. The present results demonstrate that the higher crystal-liquid interfacial free energy is a prerequisite of good GFA of the Cu-Zr alloys.