Phase-contrast computed tomography (CT) using high-brilliance, synchrotron-generated x-rays enable three-dimensional (3D) visualization of microanatomical structures within biological specimens, offering exceptionally high-contrast images of soft tissues. Traditional methods for phase-contrast CT; however, necessitate a gap between the subject and the x-ray camera, compromising spatial resolution due to penumbral blurring. Our newly developed technique, Superimposed Wavefront Imaging of Diffraction-enhanced x-rays (SWIDeX), leverages a Laue-case Si angle analyzer affixed to a scintillator to convert x-rays to visible light, capturing second-order differential phase contrast images and effectively eliminating the distance to the x-ray camera. This innovation achieves superior spatial resolution over conventional methods. In this paper, the imaging principle and CT reconstruction algorithm based on SWIDeX are presented in detail and compared with conventional analyzer-based imaging (ABI). It also shows the physical setup of SWIDeX that provides the resolution preserving second-order differential images for reconstruction. We compare the spatial resolution and the sensitivity of SWIDeX to conventional ABI. To demonstrate high-spatial resolution achievable by SWIDeX, the internal structures of four human tissues-ductal carcinoma in situ, normal stomach, normal pancreas, and intraductal papillary mucinous neoplasm of the pancreas-were visualized using an imaging system configured at the Photon Factory's BL14B beamline under the High Energy Accelerator Research Organization (KEK). Each tissue was thinly sliced after imaging, stained with hematoxylin and eosin (H&E) for conventional microscope-based pathology. A comparison of SWIDeX-CT and pathological images visually demonstrates the effectiveness of SWIDeX-CT for biological tissue imaging. SWIDeX could generate clearer 3D images than existing analyzer-based phase-contrast methods and accurately delineate tissue structures, as validated against histopathological images. SWIDeX can visualize important 3D structures in biological soft tissue with high spatial resolution and can be an important tool for providing information between the disparate scales of clinical and pathological imaging.