Using the first-principles calculations within the density functional theory, we study the nanofriction between two graphene layers. The result shows that the friction of the graphene is isotropic, and the relationship between the load and the friction factor can be divided into three phases. For the smaller and larger loads, the friction factor does not increase as the load increases, which follows the Amonton's law; for the middle phase, with the increase of the load, the friction factor increases linearly. However, the nanofriction characteristics between the two incommensurate graphenes show that the incommensurate structure can reduce the friction factor between graphenes greatly, which is in agreement with experimental result. These studies provide a fundamental understanding about the nanofriction phenomenon between the graphene layers.