In this paper we computationally investigate the magnetization for three-dimensional (3D) InAs/GaAs nanorings with different radii in an external magnetic field. Our simulation model includes: (i) the effective mass Hamiltonian in nonparabolic approximation, (ii) the position- and energy-dependent quasi-particle effective mass approximation, (iii) the finite hard wall confinement potential, and (iv) the Ben Daniel-Duke boundary conditions. The nonlinear iterative method is applied to solve the 3D problem. With the developed computer simulator, we find the magnetization for the 3D InAs/GaAs ring is a negative function and oscillates nonperiodically. The oscillation saturates when the applied magnetic filed is increased. This result provides an alternative for the nanoring energy shell structure study and is useful for spintronics applications.