For the first time, a novel technique for preparing cobalt(II) acetyl acetonate [Co(acac)₂] nanostructures has been developed by using the sublimation process. It is found that the sublimation temperature has a main role in creating the special morphology and size of [Co(acac)₂] and Co₃O₄ nanostructures. The nano-sized Co₃O₄ were obtained by thermal decomposition of [Co(acac)₂] nanostructures at 400 °C for 120 min. The produced nanostructures were characterized by powder X-ray diffraction (XRD), energy dispersive X-ray spectroscopy (EDS) analysis, Raman spectroscopy, transmission and scanning electron microscopy (TEM, SEM). Magnetic and optical properties of the final product were measured at room temperature by a vibrating sample magnetometer (VSM) and UV-vis spectroscopy, respectively. The Co₃O₄ nanostructures were anchored onto the graphene sheets and the Co₃O₄/graphene (Co₃O₄/GR) nanocomposite was synthesized through pre-graphenization successfully. To investigate the catalytic properties of Co₃O₄/G nanocomposites, photooxidation of methyl orange (MO) was performed. The performed photocatalytic test shows that the methyl orange degradation was about 54.9% after 75 min irradiation of UV light.