Our goal in this work was to study the effect of graphene nano-sheets’ size on the graphene/water nanofluid viscosity using molecular dynamics simulation. Prior to the calculation of the viscosity of the nanofluid, a validation of the computational strategy and the simulation model was tested and the results of the viscosity and density of water molecules with SPC/E, TIP3P and TIP4P potentials at 298 K were compared to the experimental data. It was found that the TIP3P potential gives better result for the viscosity, hence was used in our further calculations. Simulations were conducted at room temperature (298 K) and atmospheric pressure with the Berendsen algorithm. The system was initially run for 300 ps under the NVT conditions. Finally, the production steps of 2 ns with the integral step of 1 fs were performed. Two graphene sheets of the sizes of 20 × 20 and 10 × 10 nm2 were considered. It was observed that the viscosity of nanofluids containing smaller particles is higher than that of the nanofluids containing higher-diameter particles. Moreover, to obtain a better insight into the local structure and organization of the studied system, the site–site and center of mass radial distribution functions (RDFs) were studied. RDFs of oxygen and hydrogen atoms of water molecules were calculated. The obtained RDFs showed that distinct layers of water molecules are formed near the graphene sheet. The observed peaks in the RDF graphs show strong interactions between water molecules and graphene sheet.