We have developed X-ray refraction-based computed tomography (CT) that is able to visualize soft tissue in between hard tissue. The experimental system consists of Si(220) diffraction double-crystals and is called the DEI (diffraction-enhanced imaging) method, in which the object is located between the crystals and a CCD camera to acquire data as 360 X-ray images. The X-ray energy used was 17.5 keV. The algorithm used to reconstruct CT images was developed by A. Maksimenko and colleagues. We successfully visualized articular cartilage and the distribution of bone marrow, which are inner structures. Our method has much higher contrast compared to the conventional absorption-based CT system.