Mecanum wheel-legged robots have advantages of both wheeled mobile robots and legged robots. They can move fast with wheels, overcome challenging terrains with legs, and change heading direction or their support polygon quickly. However, for the robot to achieve dynamic motions, the controller should consider the complex dynamics derived from the robot and mecanum wheel kinematics. This paper proposes the control scheme which consists of the model predictive controller and whole-body tracking controller for the mecanum wheel-legged robot. Whole body simulation is conducted to validate the proposed controller. Hardware experiments validate its performance as well. In order to figure out the performance of the controller, the simulation and hardware tests are conducted on the following cases: keeping balance from disturbance, omnidirectional moving with narrow support polygons.