Wheeled-legged robot integrates the strong points of the legged and wheeled robot, it has the characteristics of flexible movement and strong anti-interference ability, which make it have great potential in survey, indoor service and disaster rescue scenarios. This paper design the mechanical structure, and then derive a three-dimensional dynamic model of the robot. Next, linear quadratic regulator(LQR) methods are designed to keep the balance of the robot, and the virtual model control (VMC) method is exploited to control the leg. The simulation and experimental results show that the designed linear quadratic regulator can keep the balance of the robot, while the VMC method can achieve the changes in leg posture of the robot.