In this paper, we examine the effectiveness of the interpersonal distance between a virtual robot head and humans and the gaze estimation using a display that can be viewed stereoscopically without using any wearable devices. An actual robot with a body which is like human’s body cannot always maintain an appropriate the interpersonal distance, because large movements may harm humans. To solve the problem of actual robots, onscreen agents which are displayed in a flat screen can be used. However, onscreen agents cause the Mona Lisa effect which makes humans feel gazed by agents wherever they stand. In this work, we developed a virtual robot head which is displayed in stereoscopic display. We prepared a scenario of museum tour, and asked 25 participants how far they wanted to move from the virtual museum guide robot head. They were also asked to estimate the point which they felt the virtual robot head was gazing at. As a result, it was found that the interpersonal distance was applied between the virtual robot head and the human by giving a box to the virtual robot head. It was also found that the Mona Lisa effect is reduced by giving a box to the virtual robot head and displaying it in three-dimensionally.