This paper presents tracking algorithms of a mobile robot that follows a human body moving at high speed in unstructured outdoor environment. The mobile robot, which is a differential-driven wheel type, is equipped with one laser range finder to perform high-speed human tracking and obstacle avoidance. Initially, the waist part of the human body is found the best part of the human body for robust tracking by a laser range finder. Next an obstacle avoidance algorithm considering the relative velocity between the robot and obstacles is proposed. It is shown that the proposed human tracking algorithms based on the Kalman filter performs well even in the case of the target occlusions and temporary losses. These tracking algorithms have been applied to a marathoner following robot that carries the marathoner's personal belongings in many different outdoor environments.