Four-dimensional X-ray phase tomography has been implemented by a combination of X-ray Talbot interferometry and white synchrotron radiation. While the Fourier-transform method has been used for the measurement of a differential phase image at every projection direction, an improved scan mode based on the fringe-scanning method is demonstrated to improve spatial resolution. The disadvantage of the fringe-scanning method, which requires multiple moiré images, is overcome by proposing a scan mode synchronously combining one-way continuous movements of sample rotation and grating displacement. In addition, the operation of an X-ray Talbot-Lau interferometer with white synchrotron radiation is reported. While an X-ray Talbot interferometer requires a horizontal sample rotation axis because of the condition of spatial coherency, such a horizontal rotation axis is not preferable for tomographic scans especially for soft objects. An X-ray Talbot-Lau interferometer overcomes this problem, allowing a vertical sample rotation axis. Although we encountered a vibration problem with the X-ray Talbot-Lau interferometer probably because of incomplete stage stability, our attempts have basically been successful, and we expect that various samples can be scanned by four-dimensional X-ray phase tomography, revealing dynamical properties in weakly absorbing objects that cannot be accessed by conventional X-ray phase tomography mainly performed for static samples.