Water electrolysis is regarded as the most promising method for developing sustainable energy technologies. However, low-cost bifunctional electrocatalysts with high efficacy and long-term stability are required to make this method economically viable. Core-shell nanoparticles, which comprise a thin layer of a catalytically active shell surrounding a subsurface core, have recently emerged as cutting-edge electrocatalysts for effective water electrolysis. Herein, we systematically fabricated distinct bimetallic Cu–Ni particles by tuning the Cu:Ni ratios, and then anchored them to an N-doped reduced graphene oxide (NRG) backbone for alkaline water splitting. A Cu:Ni molar ratio of 1:1 was determined to be optimal for forming an effective core–shell configuration, affording favorable adsorption energies toward reactants. The Cu–Ni(1:1) core–shell nanoparticles anchored NRG, termed Cu–Ni(1:1)@NRG, displayed excellent performance toward the H2 evolution reaction (HER) and oxygen evolution reaction (OER), with overpotentials at 10 mA cm−2 of 107 and 310 mV, respectively, versus a reversible hydrogen electrode (RHE). This current density (10 mA cm−2) was attained at a low cell voltage of 1.64 V when Cu–Ni(1:1)@NRG was used as the bifunctional electrocatalyst for alkaline water electrolysis. Furthermore, the Cu–Ni(1:1)@NRG electrocatalyst exhibited outstanding long-term stability in prolonged electrocatalytic studies at a constant current density.