We present a quantitative analysis on orbital magnetization of graphene under a magnetic field. Theenergy spectra were obtained by solving Harper equation for a honeycomb lattice. The effect of thenext-nearest-neighbor hopping(NNNH) is to increase the period of the magnetic subbands in f/f0 from 1 to 6 (where f is the magnetic flux through a unit cell and f0 is the flux quanta). The shiftsof the energy levels due to the NNNH vary with the magnetic field. The Holmholtz free energy atthe points f/f0=6n+1 is lowered as compared to that with the nearest neighbor hopping only. Forgraphene nanoribbons, the magnetic susceptibility is very sensitive to the ribbon width and chirality.The zero-field susceptibility increase with the ribbon width.