Non-interferometric X-ray quantitative phase imaging (XQPI), much simpler than the interferometric scheme, has provided high-resolution and reliable phase-contrast images. We report on implementing the volumetric XQPI images using concurrent-bidirectional scanning of the orthogonal plane on the optical axis of the Foucault differential filter; we then extracted data in conjunction with the transport-intensity equation. The volumetric image of the laminate microstructure of the gills of a fish was successfully reconstructed to demonstrate our XQPI method. The method can perform 3D rendering without any rotational motion for laterally extended objects by manipulating incoherent X-rays using the pinhole array.