There is a demand to display image on a transparent medium. If we can show image superimposed on a window, it can attract interest of people. However, a current achieved transparent displays show images only on the display surface, hence it is difficult to show image superimposed on an object that exists behind the screen. Thus, it doesn't understand intuitively. On the other hand, a display which can be perceived the image behind the screen should be placed inclined. Therefore, it is difficult to apply to advertising and exhibition. The purpose of this study is to generate transparent display to show image superimposed on near an object that exists behind the screen. We propose a display which shows image not on display surface but at a different image of depth. In this system, to show the image at behind the screen, display device is reflected on the transparent screen which incorporates a half mirror array. In this study, we use the mirror array as screen in order to locate the display device at an appropriate place. We optimize the surface of display device and angle of all mirrors so as to minimize the virtual image distortion. To confirm the practicality of the proposed method, we conducted a simulation. From the result, we confirmed the virtual image was able to display designated position.