We present a first-principles modeling study of a new class of nanomaterials in which buckminsterfullerene (C60) and graphene (G) are bridged by Cr via coordination bonds. Two nanostructures denoted as G(C54)-Cr-C60 and G(C150)-Cr-C60 are investigated, which share many similarities in the configuration geometries but differ in the distribution densities of Cr-C60 on the graphene surface. The binding energies between C60 and the rest of the system in these complexes are calculated to be 2.59 and 2.10 eV, respectively, indicative of their good structural stability. Additional spin-polarized calculations indicate that G(C54)-Cr-C60 is weakly ferromagnetic, which is chiefly due to the contribution from the 3d shell of Cr. We then investigate three model complexes of C60-Cr-G(C54) and a metal cluster (Ni4, Pd4, or Pt4). The binding energies of these three nanostructures are significantly large (3.57, 2.38, and 4.35 eV, respectively). Electron density analysis along the Ni-C, Pd-C, and Pt-C bonds consistently affirms that the Pt-C bond is the strongest while the Pd-C bond is the weakest. The strong Pt-C bond is attributed to the effective overlap of 5d(z(2)) (Pt) and 2p(z) (C) orbitals. Partial density of states analysis indicates that Ni4 and Pd4 substantially contribute to the strong ferromagnetism of the complexes, whereas Pt4 is observed to be non-magnetic even when the spin-orbit coupling is taken into account. H2 dissociation on the Ni4 complex is also examined, and the estimated reaction barrier is relatively low (0.76 eV).