Non-magnetic materials exhibiting large spin-Hall effect (SHE) are eagerly desired for high-performance spintronic devices. Here, we report that non-equilibrium Cu-Ir binary alloys with compositions beyond the solubility limit are candidates as spin-Hall materials, even though Cu and Ir do not exhibit remarkable SHE themselves. Thanks to non-equilibrium thin film fabrication, the Cu-Ir binary alloys are obtained over a wide composition range even though they are thermodynamically unstable in bulk form. We investigate the SHE of Cu-Ir by exploiting a combinatorial technique based on spin Peltier imaging, and find that the optimum Ir concentration for enhancing SHE is around 25 at.%. We achieve a large spin-Hall angle of 6.29 ± 0.19% for Cu76Ir24. In contrast to Cu-Ir, non-equilibrium Cu-Bi binary alloys do not show remarkable SHE. Our discovery opens a new direction for the exploration of spin-Hall materials.