Design and synthesis of green and recyclable catalysts in order to improve the efficiency of organic chemistry reactions is a significant challenge. One of these reactions is the homocoupling reaction of terminal alkynes, known as the Glaser coupling reaction. In this study, first, graphitic carbon nitride (g-C3N4) nanosheets with high surface area and chemical stability were synthesized. Afterwards, the surface of this nano-substrate was modified with polyethyleneimine as a chelating agent to obtain g-C3N4/PEI. Finally, copper(I) was added to the nanocomposite, and the Cu(I)@g-C3N4/PEI catalyst was synthesized. The active site of copper(I) in this catalyst was calculated to be 0.16 mol in 100 g Cu(I)@g-C3N4/PEI. The synthesized catalyst was characterized by different methods such as FTIR, XRD, ICP, SEM, EDX, and mapping. Also, a deep eutectic solvent (a mixture of choline chloride and urea) was synthesized and used as a green solvent in this reaction. The reaction was performed at 100 degrees C for 30 min, and the yield was obtained as 90%. The advantages of this reaction include easy catalyst separation and reusability thanks to its heterogeneous nature, the use of a deep eutectic solvent as a green solvent, which results in a clean reaction with good to excellent efficiency, and finally short reaction time.