The two-wheeled legged robot combines the advantages of legged robot and wheeled robot and has high terrain adaptability. Spherical robots are highly resistant to interference during detection. In this paper, a new sphere-wheel-legged robot is designed by combining these three motion modes. This paper begins by introducing the mechanical design, hardware, and software. Then, kinematics and dynamics of wheel-legged motion and spherical motion are analyzed in detail. Subsequently, the controllers for wheel-legged balancing motion, wheel-legged jumping motion, and sphere rolling motion are developed, respectively. Finally, experiments are carried out for different modes. The results demonstrate that the designed robot has excellent locomotor capabilities over different terrains.