Visualizing objects as they are perceived in the real world is often critical in our daily experiences. We previously focused on objects' surface glossiness visualized with a 3D display and found that a multi-view 3D display reproduces perceived glossiness more accurately than a 2D display. This improvement of glossiness reproduction can be explained by the fact that a glossy surface visualized by a multi-view 3D display appropriately provides luminance differences between the two eyes and luminance changes accompanying the viewer's lateral head motion. In the present study, to determine the requirements of a multi-view 3D display for the accurate reproduction of perceived glossiness, we developed a simulator of a multi-view 3D display to independently and simultaneously manipulate the viewpoint interval and the magnitude of the optical inter-view crosstalk. Using the simulator, we conducted a psychophysical experiment and found that glossiness reproduction is most accurate when the viewpoint interval is small and there is just a small (but not too small) amount of crosstalk. We proposed a simple yet perceptually valid model that quantitatively predicts the reproduction accuracy of perceived glossiness.