Payload capacity and transition ability are essential for climbing robots to apply the robots to various applications such as inspection and exploration. This paper presents a new climbing robotic platform with multi-link structure of track-wheel modules to enhance payload capacity and transition ability, and its tracking controller design and experimental results. The compliances between track-wheel modules achieve stable internal and external transitions while the large adhesion area of the track-wheel module enhances the payload capacity of the robot. Kinematic model-based tracking controller is designed and implemented for autonomous internal transition, and the gains of the controller are optimized by experimental design. Experiments on the automatic internal transitions are performed and the results guarantee autonomous internal transition with little tracking error.