A high-efficiency graphene oxide-terminated hyperbranched amino polymer-carboxymethyl cellulose ternary nanocomposite (GO-HBP-NH-CMC) was fabricated for adsorbing heavy metals from aqueous solutions. The adsorbent was characterized by SEM, FT-IR, Raman, and XPS analyses showing its porous architecture, rough surface, abundant N- and O-containing functional groups providing enhanced binding ability towards Pb and Cu. Experimental adsorption data fitted well to the pseudo-second-order kinetics and Langmuir isotherm models, indicating the adsorption of GO-HBP-NH-CMC towards Pb and Cu being a chemical and monolayer process. The maximum adsorption capacities of GO-HBP-NH-CMC for Pb and Cu at 25 °C comprised 152.86 and 137.48 mg/g, respectively. The laboratory-scale experimental study into the Pb and Cu adsorption in a fixed-bed column was undertaken. Effects of flow rate, bed depth and influent metals concentration on the adsorption performance were assessed. Experimental data successfully correlated with the Adams-Bohart, Thomas and Yoon-Nelson models with the R exceeding 0.79. Density functional theory calculation was adopted to study interactions between functional groups at GO-HBP-NH-CMC and heavy metals showing OH, NH and COOH moieties in GO-HBP-NH-CMC being more likely to bind Pb rather than Cu, while the binding abilities of -CONH- towards Pb and Cu were similar.