A multi-DOF two-wheeled robot is considered, the research is aimed to develop the dynamic model and balance control scheme of the robot. A balance weight is involved to compose a new DOF, the dynamic model of the robot is established with Lagrange equations. To facilitate the modelling and design control scheme, the dynamic model is simplified and the displacement of balance weight is chosen as control input instead of state variable. With the dynamic model, a LQR controller is designed for achieving the desired velocity of the robot while stabilizing the central body. Simulation and physical prototypes are established to prove the veracity of the model and confirm the validity of the designed controller.