Graphene has received a lot of attention for its excellent physical and chemical properties, and the unique wettability of graphene is still under investigation. Most of previous studies focused on graphene or carbon nanotubes, and less of them on the comparison of wettability between graphene and other materials to reveal the characteristic wettability of graphene. In the present study, the wettability of monolayer graphene, copper and silica are studied by using the molecular dynamics simulation, in which the contact angle and the water molecule arrangement (i.e. density distribution and angle distribution of water molecules) on the substrates are analyzed. The results show that although both copper and graphene are weak hydrophilic materials, there are two neat layers of water molecule structure on the surface of graphene, and water molecules are disordered on the surface of copper. Silica is a kind of strong hydrophilic material and graphene is a kind of weak hydrophilic material, but both of them have two layers of dense water molecule layer, which are in different states, on the surface. On the silica surface, the two layers of water molecules, whose densities are greatly different, are close to the substrate, and hydrogen bonds are randomly arranged, which is very different from the arrangement of water molecules on the graphene surface. By making a comparison of wettability among the three materials, the characteristic water molecule arrangement on graphene surface is obtained: there exist two layers of water molecules on the surface of graphene. Within the dense layer of water molecules near the substrate, the angles between the O−H bonds of water molecule and the vertical direction of substrate focus on 90°, while the hydrogen bonds on the surface are almost perpendicular to the substrate. Furthermore, it is found that adding a layer of graphene on copper (the main force between water molecules and copper is van der Waals force) will have a less influence on copper wettability. However, adding a layer of graphene on silica (the main force between water molecule and silica is from chemical bonds) will have a significant influence on the wettability of silica, i.e. not only the upper contact angle increases significantly, but also the arrangement of water molecules on the surface of the substrate becomes similar to that of graphene. These simulated results are found to be in agreement with the experimental results of Rafiee et al. [Rafiee J, Mi X, Gullapalli H, Thomas A V, Yavari F, Shi Y, Ajayan P M, Koratkar N A 2012 Nature 11217]. This work can provide a theoretical guidance for further developing the applications of graphene in microstructure design.