A special adsorption of Cu2+ removal is demonstrated using specifically functionalized graphene oxide (GO)/isocyanate (MDI) composites, on which ethylenediamine tetraacetic acid (EDTA) is grafted via amidation and carbamate reaction. The structure and morphology of GO and functionalized composites (EDTA/MDI/GO) were characterized by scanning electron microscope (SEM), Fourier transform infrared spectra (FT-IR), X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS) and Thermogravimetric analysis (TGA). This study investigated the adsorption and desorption behaviors of heavy metal cations and the effects of solution conditions such as pH on Cu2+ removal. The experimental results illustrated that after introducing EDTA and MDI into the GO, the maximum adsorption capacity reached 254.2 ± 10.4 mg/g within 180 min, obviously higher than the GO prepared without these additions (136.5 ± 7.2 mg/g). The EDTA/MDI/GO adsorption kinetics and equilibrium adsorption isotherm fitted the pseudo-second-order kinetic model (R2 = 0.995) and Langmuir isotherm model (R2 = 0.986) well, respectively. Furthermore, EDTA/MDI/GO also displayed good reusability for the efficient removal of Cu2+ after being washed with HCl, suggesting potential application in Cu2+ cleanup.