Using the first-principles calculations within density functional theory, we have studied the nanofriction between two graphene layers.It showed that the friction of the graphene is isotropic,and the relationship between the load and the friction factor can be divided into three phases.However, the nanofriction character between the two incommensurate graphene showed that the incommensurate structure can reduce the friction factor between graphenes greatly, in agreement with experiments.Compared with clean graphene, the coefficients of friction decrease greatly due to electrons accumulating between carbon and attached hydrogen atoms, leading to the significant decrease of the potential energy of the single side hydrogenated graphene.Thess studies provide a fundamental understanding about the nanofriction phenomenon between the grapheme layers.