The design of a highly efficient and durable electrocatalyst for the production of hydrogen via electrochemical water splitting is highly desirable but remains a tremendous challenge. Though there has been some progress in basic media wherein the reaction is sluggish, here we report the synthesis of a new hybrid catalyst comprising Cu and Rh elements as bimetallic single atoms (SAs) and nanoparticles (NPs) on a N-doped graphene (G_N) surface (1: Cu/Rh(SAs) + Cu₂Rh(NPs)/G_N) that works remarkably fast for the hydrogen evolution reaction (HER) in acidic media. Benefiting from the large specific electrochemical surface area, low charge transfer resistance and combined synergistic effect of bimetallic SAs and NPs, the as-obtained catalyst 1 requires an overpotential as low as 8 mV (commercial Pt/C requires 14 mV) in 0.5 M H₂SO₄ solution to deliver a benchmark current density of 10 mA cm⁻². It maintains constant current densities (∼10–100 mA cm⁻²) at both low and high overpotentials during the 500 h continuous HER electrolysis chronoamperometry test. Moreover, 1 exhibits a low Tafel slope (27 mV dec⁻¹), a high turnover frequency and mass activity (1.237 s⁻¹ and 2.314 A mg_Rh⁻¹) which are higher than those of Pt/C (0.329 s⁻¹ and 0.326 A mg_Pt⁻¹) and a constant H₂ production rate with high faradaic efficiency (98–99%). Electrochemical experiments in conjunction with density functional theory (DFT) calculations reveal that the combination of Rh and Cu atoms on the G_N surface not only maximizes the rates of H⁺ adsorption on the electrode surface (due to the high surface area of 1) but also optimizes the hydrogen adsorption free energy (ΔG_H*) close to zero (0.01 eV), improving the intrinsic catalytic activity for the HER.