Photocatalytic degradation of dyes has been the subject of extensive study due to its low cost, eco-friendly operation, and absence of secondary pollutants. Copper oxide/graphene oxide (CuO/GO) nanocomposites are emerging as a new class of fascinating materials due to their low cost, nontoxicity, and distinctive properties such as a narrow band gap and good sunlight absorbency. In this study, copper oxide (CuO), graphene oxide (GO), and CuO/GO were synthesized successfully. X-ray diffractometer (XRD) and Fourier transform infrared (FTIR) spectroscopy confirm the oxidation and production of GO from the graphene of lead pencil. According to the morphological analysis of nanocomposites, CuO nanoparticles of sizes ≤20 nm on the GO sheets were evenly adorned and distributed. Nanocomposites of different CuO:GO ratios (1:1 up to 5:1) were applied for the photocatalytic degradation of methyl red (MR). CuO:GO(1:1) nanocomposites achieved 84% MR dye removal, while CuO:GO(5:1) nanocomposites achieved the highest value (95.48%). The thermodynamic parameters of the reaction for CuO:GO(5:1) were evaluated using the Van't Hoff equation and the activation energy was found to be 44.186 kJ/mol. The reusability test of the nanocomposites showed high stability even after seven cycles. CuO/GO catalysts can be used in the photodegradation of organic pollutants in wastewater at room temperature due to their excellent properties, simple synthesis process, and low cost.