Quantitative measurements of the phase shift of X-rays passing through a matter allow us to perform X-ray phase tomography for visualization of soft materials. Combination of an X-ray microscope and a grating interferometer is a promising approach to realize quantitative phase measurements with a microscopic spatial resolution. A Lau interferometer consisting of a source grating and a phase grating is available for this purpose with an incoherent laboratory X-ray source. We installed a Lau interferometer into a laboratory-based X-ray microscope adopting a copper rotating anode source and Fresnel zone plates (ZEISS Xradia 800 Ultra). A "twin-phase image", which consists of positive and negative phase images overlaid with a certain separation, is generated through a fringe-scanning measurement with this microscope. A step for generating a quantitative phase image from the twin phase image should be developed to perform phase tomography. However, conventional deconvolution operations are not suitable because of artifacts and noise remained in resultant phase images. To reduce the artifacts and noise, an iterative calculation algorithm has been developed. The evaluation of the algorithm shows that the artifacts and noise are suppressed and quantitative phase images are obtained. Finally, results of phase tomography obtained for soft materials are demonstrated.