Properties of metal elements can be modified by alloying. Given that catalytic efficiencies are often maximized using metal single-atoms (SAs), two immiscible metals can improve the catalytic activity when they can be present as non-agglomerated dual SAs. Here, we report yet-unexplored synthesis of high-performance electro-catalysts utilizing immiscibility of Cu/Ru bimetal atoms. In the synthesized electrocatalyst (Cu/Ru@G(N)), both Cu-SAs and Ru-SAs are dispersed on N-doped graphitic-matrix (GN), while other Cu-SAs are bridged to Ru nanoparticles (NPs) surface via nitrogen. It shows superior mass-activity with outstanding catalytic performance and durability for hydrogen evolution reaction (HER), outperforming commercial Pt-20wt%/C. Cu-SAs along with Ru-NPs enhance electric conduction or charge-transfer rate of GN-templates for fast kinetics. Owing to Cu-Ru immiscibility, the coordination of Cu-SAs by N atoms which bridge to Ru-NPs surface, introduces new active sites and brings about long-term stability (over 600 h in acidic media) by preventing aggregation of Ru-NPs.