This paper presents a human detection algorithm and an obstacle avoidance algorithm for a marathoner service robot (MSR) that provides a service to a marathoner while training. To be used as a MSR, the mobile robot should have the abilities to follow a running human and avoid dynamically moving obstacles in an unstructured outdoor environment. To detect a human by a laser range finder (LRF), we defined features of the human body in LRF data and employed a support vector data description method. In order to avoid moving obstacles while tracking a running person, we defined a weighted radius for each obstacle using the relative velocity between the robot and an obstacle. For smoothly bypassing obstacles without collision, a dynamic obstacle avoidance algorithm for the MSR is implemented, which directly employed a real-time position vector between the robot and the shortest path around the obstacle. We verified the feasibility of these proposed algorithms through experimentation in different outdoor environments.