It is a challenge to generate stereoscopic (3D) video through a single moving camera under widely varying conditions. We propose an efficient approach to create true stereoscopic video from a monocular video stream captured under various moving conditions. The approach contains three major steps. First, we apply Harris' corner detector to detect distinctive feature points from a pair of image frames selected from the incoming video captured by a moving camera. Second, according to the consecutive property of the video, a local-window search based algorithm is developed for fast and accurate feature correspondence between the two image frames. Third, a hierarchical image rectification technique is designed to guarantee the success in creating a true and visually-comfortable stereo image for each incoming image frame. Besides, a software-based video stabilization algorithm is also developed for improved stereo video generation performance. Extensive tests using real video collected under various situations were performed for performance evaluation of the proposed approach.