3D display systems without glasses are preferred because of the inconvenience wearing of special glasses while viewing 3D content. In general, non-glass type 3D displays work by sending left and right views of the content to the corresponding eyes depending on the user position with respect to the display. Since accurate user position estimation has become a very important task for non-glass type 3D displays, most of such systems require additional hardware or suffer from low accuracy. In this paper, an accurate user position estimation method using a single camera for non-glass type 3D display is proposed. As inter-pupillary distance is utilized for the estimation, at first the face is detected and then tracked using an Active Appearance Model. The pose of face is then estimated to compensate the pose variations. To estimate the user position, a simple perspective mapping function is applied which uses the average of the inter-pupillary distance. For accuracy, personal inter-pupillary distance can also be used. Experimental results have shown that the proposed method successfully estimated the user position using a single camera. The average error for position estimation with the proposed method was small enough for viewing 3D contents.