In this paper, we deal with two types of control problems for a 3D space robot of two rigid bodies with an initial angular momentum. In our previous work, we studied a near-optimal control approach to the state transition control problem for the 3D space robots with initial angular momenta. However, for the approach, we need huge computation amount and other control purposes cannot be treated. In order to overcome these disadvantages, in this paper we apply model predictive control to the attitude stabilization control problem and the trajectory tracking control problem for a 3D universal joint space robot with an initial angular momentum. As a results of simulations, we can see that both attitude stabilization control and trajectory tracking control for the 3D space robot are accomplished by the model predictive control approach. Moreover, it can be also confirmed that this approach considerably reduces computation amount and achieves real-time control of the 3D space robot.