We study the orbital magnetism of graphene monolayer and multilayers within the effective mass approximation. For any layer numbers, the Hamiltonian and thus magnetic susceptibility can be decomposed into contributions from subsystems equivalent to monolayer or bilayer graphene. The monolayer-type subband exists only in odd-layer graphenes giving a singular susceptibility expressed by a delta function in the Fermi energy εF, while the bilayer-type subband exhibits a less singular, logarithmic peak in εF. We also study the orbital diamagnetism in non-uniform magnetic fields for monolayer graphene. We calculate within linear response theory an electric current induced by an external magnetic field with general wave number, to estimate the repulsive force between graphene and an arbitrary magnetic object located above. The magnitude of the force is much greater than that of conventional two-dimensional system, while it disappears with the increase of κF.