In this research, to remove sulfur and nitrogen compounds from heavy naphtha, various nanocatalysts were prepared through supporting NiMo over nanoporous graphene and evaluated in hydrodesulfurization and hydrodenitrogenation reactions. The nanoporous graphene was initially functionalized in order to facilitate the metal being loaded on it. Three different methods were used to functionalize the nanoporous graphene. The NiMo/nanoporous graphene nanocatalysts were characterized by field emission scanning electron microscopy, Fourier transform infrared spectroscopy, X-ray diffraction, inductively coupled plasma optical emission spectrometry, temperature-programmed reduction, nitrogen adsorption–desorption isotherms and transmission electron microscopy techniques. Catalyst performance was evaluated in terms of conversions of sulfur, mercaptans (R-SH) and nitrogen compounds. It was found that the functionalized nanoporous graphene support could significantly enhance the catalytic performance in comparison with the industrial NiMo/alumina catalyst. Among the functionalized graphene supports, amine-functionalized graphene exhibited the best results. By using NiMo supported over amine-functionalized graphene, the conversions of total sulfur and R-SH reached 97.8% and 98.1%, respectively.