In this paper, we present an algorithm for a shape-shifting robot climbing stairs autonomously. The robot has been used several times for search and rescue missions. Because of the special environment of tasks, the robot must have the ability to climb stairs autonomously to help the operators. Due to the characters of robot in "T" configuration, the mathematical model of force is established and the whole process of climbing stairs is analyzed. Grouser-tread hooking, track-stair edge frictional force et al. are all considered during the process of climbing. A description of its dynamic model is also presented which is involved in the controller. The controller is comprised of center control and heading control, which can help the robot climb stairs safely and quickly. The effectiveness of the algorithms proposed are verified by experiment.