An X-ray Talbot-Lau interferometer scanning setup consisting of three transmission gratings, a laboratory-based X-ray source that emits X-rays vertically, and an image detector on the top has been developed for the application of X-ray phase imaging to moving objects that cannot be tested clearly with conventional absorption contrast. The grating-based X-ray phase imaging method usually employs a phase-stepping (or fringe-scanning) technique by displacing one of the gratings step-by-step while the object stays still. Since this approach is not compatible with a scanner-type application for moving objects, we have developed a new algorithm for achieving the function of phase-stepping without grating displacement. By analyzing the movie of the moiré pattern as the object moves across the field of view, we obtain the absorption, differential phase, and visibility images. The feasibility of the X-ray phase imaging scanner has been successfully demonstrated for a long sample moving at 5 mm/s. This achievement is a breakthrough for the practical industrial application of X-ray phase imaging for screening objects carried on belt-conveyers such as those in factories.