Abstract-An omnidirectional mobile manipulator, due to its large-scale mobility and dexterous manipulability, has attracted lots of attention in the last decades. However, modeling and control of such a system are very challenging because of its complicated mechanism.In this paper, we achieve the kinematics of the mobile platform according to its mechanical structure firstly, and then deduce its unified dynamic model by Lagrangian formalism. By applying the unified model to calculate the coupling torque vector between the mobile platform and the robot arm, an adaptive hybrid controller is proposed subsequently. This controller consists of two parts: one is responsible for the tracking control of the mobile platform in kinematics. The other part is for the robot arm in dynamics. For further consideration of unmodeled dynamics and external disturbances, a Radial Basis Function Neural-Network (RBFNN) is adopted in the adaptive controller. Simulation results show the correctness of the presented model and the effectiveness of the control scheme.