We present a image quality improvement in a parallax barrier (PB)-based multiview autostereoscopic 3D display system under a real-time tracking of positions of a viewer's eyes. The system presented exploits a parallax barrier engineered to offer significantly improved quality of three-dimensional images for a moving viewer without an eyewear under the dynamic eye tracking. The improved image quality includes enhanced uniformity of image brightness, reduced point crosstalk, and no pseudoscopic effects. We control the relative ratio between two parameters i.e., a pixel size and the aperture of a parallax barrier slit to improve uniformity of image brightness at a viewing zone. The eye tracking that monitors positions of a viewer's eyes enables pixel data control software to turn on only pixels for view images near the viewer's eyes (the other pixels turned off), thus reducing point crosstalk. The eye tracking combined software provides right images for the respective eyes, therefore producing no pseudoscopic effects at its zone boundaries. The viewing zone can be spanned over area larger than the central viewing zone offered by a conventional PB-based multiview autostereoscopic 3D display (no eye tracking). Our 3D display system also provides multiviews for motion parallax under eye tracking. More importantly, we demonstrate substantial reduction of point crosstalk of images at the viewing zone, its level being comparable to that of a commercialized eyewear-assisted 3D display system. The multiview autostereoscopic 3D display presented can greatly resolve the point crosstalk problem, which is one of the critical factors that make it difficult for previous technologies for a multiview autostereoscopic 3D display to replace an eyewear-assisted counterpart.