Based on the Anderson impurity model and self-consistent approach,we investigate the condition for the screening of a local magnetic moment by electrons in graphene and the influence of the moment on electronic properties of the system.The results of numerical calculations carried out on a finite sheet of graphene show that when the Fermi energy is above the single occupancy energy and below the double occupancy energy of the local impurity,a magnetic state is possible.A phase diagram in a parameter space spanned by the Coulomb energy U and the Fermi energy is obtained to distinguish the parameter regions for the magnetic and nonmagnetic states of the impurity.We find that the combined effect of the impurity and finite size effect results in a large charge density near the edges of the finite graphene sheet.The density of states exhibits a peak at the Dirac point which is caused by the appearance of the edge states localized at the zigzag edges of the sheet.