Spherical mobile robots belong to a class of mobile robots which may have applications ranging from exploration to entertainment. This paper presents our preliminary kinematic study of spherical mobile robots which are driven by an omni-wheel based internal driving unit (IDU). At first, we discuss the conceptual design of spherical mobile robots with an omni-wheel based IDU. Several IDUs are proposed. Then we derive the velocity equation of a spherical mobile robot with an omni-wheel based IDU. Finally, two isotropic configurations of spherical mobile robots with an omni-wheel based IDU are identified. This work lays the foundation for the further investigation on spherical mobile robots with an omni-wheel based IDU.