In developing a user interface, it is very important to provide usability, intuitiveness and convenience. To accomplish these factors, 3D user interface can be one good solution. Recently, many kinds of embedded devices have been developed and utilized for various areas of human life; for example, Digital TVs, game consoles, MP3 players, etc. A GUI makes these devices easier to use and more effective. But, their poor hardware performances often prevent developing a high quality visual effect on their GUIs. A visual effect using alpha blended object is one of the typical examples of this kind that limits the development of 3D applications on an embedded hardware. In this paper, we propose an effective object sorting technique that can be used to develop a 3D GUI including many translucent objects.