For an auto-stereoscopic 3D display, the viewing image quality depends on the viewing position of the observer. Therefore, viewing zone is one of the most important issues for auto-stereoscopic 3D displays. Though there are lots of studies, deeper researches are still needed for further understanding. In this study, we propose a novel non-imaging method to evaluate the viewing zone by analytic formula and discuss the affecting factors for the viewing zone of parallax-barrier type auto-stereoscopic 3D displays.