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Abstract The wheel-legged hybrid structure has been utilized by ground mobile platforms in recent years to achieve good mobility on both flat surfaces and rough terrain. However, most of the wheel-legged robots only have one-directional obstacle-crossing ability. During the motion, most of the wheel-legged robots’ centroid fluctuates violently, which damages the stability of the load. What’s more, many designs of the obstacle-crossing part and transformation-driving part of this structure are highly coupled, which limits its optimal performance in both aspects. This paper presents a novel wheel-legged robot with a rim-shaped changeable wheel, which has a bi-directional and smooth obstacle-crossing ability. Based on the kinematic model, the geometric parameters of the wheel structure and the design variables of the driving four-bar mechanism are optimized separately. The kinetostatics model of the mobile platform when climbing stairs is established to determine the body length and angular velocity of the driving wheels. A prototype is made according to the optimal parameters. Experiments show that the prototype installed with the novel transformable wheels can overcome steps with a height of 1.52 times of its wheel radius with less fluctuation of its centroid and performs good locomotion capabilities in different environments.