We are attempting to expand the technology of X-ray grating phase imaging/tomography to enable dynamic observation. X-ray phase imaging has been performed mainly for static cases, and this challenge is significant since properties of materials (and hopefully their functions) would be understood by observing their dynamics in addition to their structure, which is an inherent advantage of X-ray imaging. Our recent activities in combination with white synchrotron radiation for this purpose are described. Taking advantage of the fact that an X-ray grating interferometer functions with X-rays of a broad energy bandwidth (and therefore high flux), movies of differential phase images and visibility images are obtained with a time resolution of a millisecond. The time resolution of X-ray phase tomography can therefore be a second. This study is performed as a part of a project to explore X-ray grating interferometry, and our other current activities are also briefly outlined.