Sphere-shaped robots are expected to be useful in that they can move around in home or office environments without getting stuck even in a dusty room with a lot of obstacles. Besides, it is desirable that one can move omni-directionally and that its body has enough space to carry additional functions such as sensors. Until now, various types of sphere-shaped robot have been proposed and studied. However, few of them satisfy both the requirements at the same time. Thus, this study proposes a new driving scheme employing an omni-directional three-wheel internal unit, in order to make it capable of moving omni-directionally providing large inner space. Then, for constant velocity movements, conditions for speed references of three wheels are derived, so that the internal unit runs smoothly without making any slippage against the inner surface of the sphere. Finally, a prototype robot is developed and the validity of the conditions is examined through experiments.