Nowadays, transition-metal adatoms and dimers with giant magnetic anisotropy have attracted much attention due to their potential applications in data storage, spintronics and quantum computations. Using density-functional calculations, we investigated the magnetic anisotropy of the rare-earth adatoms and dimers adsorbed by graphene oxide. Our calculations reveal that the adatoms of Tm, Er and Sm possess giant magnetic anisotropy, typically larger than 40 meV. When the dimers of (Tm,Er,Sm)-Ir are adsorbed onto graphene oxide, the magnetic anisotropy even exceeds 200 meV. The magnetic anisotropy can be tuned by the external electric field as well as the environment.