A life-support service robot must avoid both static and dynamic obstacles for working in a real environment. Here, a static obstacle means an obstacle that does not move, and a dynamic obstacle is the one that moves. Assuming the robot is following a target person, we discuss how the robot avoids a crowd through which the target person passes and arrives at the target position. The purpose of this paper is to propose a crowd avoidance method that makes a robot to be able to avoid both static and dynamic obstacles. The method uses the surface points of the obstacles to form an avoidance region, and the robot moves along the edge of the region. We conducted experiments assuming various situations such that the robot was blocked, there was a wide gap in the crowd, or a person in the crowd yielded for the robot to pass through. As an experimental result, it was confirmed the robot could avoid the crowd even when the obstacles were aligned in an "inverted wedge" shape.