Graphene is a 2D material that has attracted much attention due to its outstanding properties. Because of its high surface area and unique chemical and physical properties, graphene is a good candidate for biological applications. For this reason, a deep understanding of the mechanism of interaction of graphene with biomolecules is required. In this study, theoretical investigation of van der Waals effects has been conducted using density functional theory. Here we show that the order of the binding energies of five nucleobases with graphene is G > A > T > C > U. This trend is in good agreement with most of the theoretical and experimental data. Also, the effects of charging on the electronic and structural properties of the graphene-nucleubase systems are studied for the first time. We show that the binding energy can be changed by adding or removing an electron from the system. The results presented in this work provide fundamental insights into the quantum interactions of DNA with carbon-based nanostructures and will be useful for developments in biotechnology and nanotechnology.