In this paper, the development of a three-dimensional (3-D) odometry system for wheeled robots on loose soil in an application of planetary exploration is described. When a wheeled robot operates in a slippery environment, visual odometry, which is used to obtain flow images of the ground with a CCD camera, is effective for the measurement of motion because it is a non-contact method. However, in the target condition, a measurement result with a conventional camera is not reliable with this method because the viewing area of the ground varies as a result of the changing distance between the camera and the ground as a result of the wheels sinking in loose soil. To solve this problem, we used a telecentric camera for visual odometry. The lens of the camera robustly maintains the same field of view, regardless of the distance between the camera and the ground. Using the camera, we developed a (3-D) odometry system for our mobile robot to enable its positioning and navigation, and we validated the system with several experiments. In this paper, a structure and a performance test of the developed system is described. After that, the results of experiments in indoor (sandbox) and outdoor (seashore) environments are introduced.