This paper reports the results of the design and modeling of a hierarchical control system for ITER plasma shape, position and current. The system contains three hierarchy levels. The first level is a model correcting loop with a feedback constant matrix. The second level consists of two loops: a fast SISO plasma vertical position stabilization loop and a slow MIMO plasma current and shape control loop. Both loops have the controllers which were designed by an H∞ loop shaping approach in the framework of the disturbance rejection configuration. The third level is a structure with a Model Predictive Controller for improving the plasma shape control process by a vertical position reference adjustment during a plasma discharge. The main idea of our proposal is to solve a tokamak plasma vertical position instability problem in cooperation with the plasma shape and current MIMO control loop. The plasma vertical position stabilization technique provides a more reliable control system in whole when compared with the known system approach when a plasma vertical speed is stabilized at about zero. The simulation results of the plasma magnetic hierarchical control system obtained on plasma-physics nonlinear DINA code for ITER are presented. The system was modeled on DINA code on the divertor phase of the plasma current ramp-up stage and on a DINA linearized model on the flat-top phase when a minor disruption occurs.