  We study the property of a magnetic impurity on a single-layer graphene
within an Anderson impurity model. Due to the vanishing local density of states
at the Fermi level in graphene, the impurity spin cannot be effectively
screened out. Treating the problem within the Gutzwiller approximation, we
found a region in the parameter space of $U$-$E^f$ where the impurity is in the
local moment state, which is characterized by a zero effective hybridization
between the bath electron and the magnetic impurity. Here $U$ is the onsite
Coulomb repulsion of the impurity electrons and $E^f$ the impurity energy
level. The competition between $U$ and $E^f$ is also discussed. While larger
$U$ reduces double occupation and favors local moment formation, a deeper
impurity level prefers double occupation and a nonzero hybridization and thus a
Kondo screened state. For a fixed $U$, by continuously lowering the impurity
level, the impurity first enters from a Kondo screened state into a local
moment state and then departs from this state and re-enters into the Kondo
screened state.
