  We study the orbital magnetism of graphene ribbon in the effective-mass
approximation, to figure out the finite-size effect on the singular
susceptibility known in the bulk limit. We find that the susceptibility at T =
0 oscillates between diamagnetism and paramagnetism as a function of Fermi
energy, in accordance with the subband structure formed by quantum confinement.
In increasing T, the oscillation rapidly disappears once the thermal broadening
energy exceeds the subband spacing, and the susceptibility approaches the bulk
limit i.e., a thermally broadened diamagnetic peak centered at zero energy
point. The electric current supporting the diamagnetism is found to flow near
the edge with a depth which proportional to reciprocal of T, with v being the
band velocity, while at T = 0 the current distribution spreads entirely in the
sample reflecting the absence of the characteristic wavelength in graphene. The
result is applied to estimate the three-dimensional random-stacked multilayer
graphene, where we show that the external magnetic field is significantly
screened inside the sample in low temperatures, in a much stronger manner than
in graphite.
