We put forward a novel proposition that a mechanism can move in a constant direction and change its moving directions only by one actuator and construct a single-DOF (degree of freedom) ground mobile mechanism based on the well-known Schatz mechanism. This ground mobile Schatz mechanism has six links, one of which is designed as a spoke octahedron and an other one as a tail link. When the actuator rotates in one direction, the spoke octahedron can roll on the ground to let the ground mobile Schatz mechanism to move in a straight line pushed by the tail link. When the actuator rotates in the opposite direction, the tail link can be lifted to change its landing point and the relative position between it and the spoke octahedron, then the spoke octahedron can roll in another direction pushed by the tail link. In addition, it is also an untraditional application of the Schatz mechanism that it is used as a novel ground mobile mechanism. Locomotion analysis, gait planning and stability analysis are performed, respectively, and a prototype is developed and tested.