In the present research, a magnetic nanostructure based on graphene oxide and iron oxide modified by the amino acid tryptophan was synthesized. The properties of the adsorber were determined using a Fourier transform infrared spectrometer, elemental analysis, X-ray diffraction, scanning electron microscope, and vibrating-sample magnetometer. Optimum parameters such as pH, contact time, amount of used adsorbent, initial concentration of copper ions, and the effect of temperature were investigated. Adsorption isotherm studies were conducted using the Langmuir and the Freundlich models, in which the Langmuir isotherm model was more consistent in the adsorption process. The theoretical maximum adsorption capacity of the adsorbent is 125 mg of copper per gram of adsorbent, which is close to the maximum adsorption capacity of the adsorbent in the real state (118 mg of copper per gram of adsorbent). To investigate the thermodynamics of adsorption, the Van't Hoff Equations were used, the results of which indicate that the adsorption process is endothermic. Meanwhile, the removal rate of copper ions from the real wastewater sample in the presence of other ions was determined to be 46%.