Graphene stratiform membrane materials have been recently applied to heavy metal removal in aqueous systems via adsorption due to their high mechanical strength, chemical stability, and other properties. We applied reduced graphene oxide (rGO) alone as an adsorbent to remove heavy metal ions from wastewater. Self-supported rGO membrane was prepared using a green reduction method with sodium hydrosulfite. We used the Raman spectra to observe the structure of the rGO membrane. The morphology of the self-supported membrane was measured by a scanning electron microscope. The Cu²⁺ adsorption performance was measured in terms of pH, reaction time, metal ion concentration, and temperature. The maximum Cu²⁺ adsorption capacity of the rGO membrane was found to be 149.25 mg/g. The adsorption process followed a pseudo-second-order kinetic model, and adsorption isotherms were simulated by the Freundlich model.