Telepresence robots using traditional video chats do not yet fully represent the presence of a remote user. To enhance that presence, we propose a novel approach that replaces the background of the remote user with a real-time captured image of the area behind the robot. We assumed that the background of the remote user, which was visible on the telepresence robot's display, was one reason for the reduction in presence because it might remind local viewers that the remote user is in another place. We found that our approach effectively enhanced the presence of remote user and reduced the negative impression of a delay. In this paper, we describe the new approach, its implementation, and an evaluation of the system. We evaluated the subjective impressions of communication through the proposed system. This approach also protects the privacy of the remote user and makes it more acceptable to people using telepresence robots from private places, e.g., a sickroom in a hospital.