Recent development shows that carbon-based composites are proving to be the most promising materials in hydrogen energy production, storage and conversion applications. In this study, composites of the copper-based metal-organic framework with different ratios of graphite oxide have been prepared for hydrogen storage application. The developed materials are characterized by X-ray diffraction (XRD), gravimetric thermal analysis (TGA), scanning electron microscopy (SEM) and BET. The newly developed composites have an improved crystalline structure and an increased surface area. The results of the experiment showed that the composite material MOF/GO 20% can store 6.12% of hydrogen at −40 °C.