In-line X-ray phase-contrast computed tomography (IL-PCCT) can produce highcontrast and high-resolution images of biological samples, and it has a great advantage with regard to imaging the microstructures and morphologies of fibrous biological tissues (FBTs). Filtered back projection (FBP) is widely used in ILPCCT. However, it requires long scanning times and high radiation doses to produce high-quality CT images, and this restricts its applicability in biomedical and preclinical studies on FBTs. To solve this problem, a novel IL-PCCT reconstruction algorithm is proposed to decrease the radiation dose by reducing the number of projections and reconstruct high-quality CT images of FBTs. The proposed algorithm incorporates the FBP method into the iterative reconstruction framework. Considering the area types and anisotropic edge properties of FBTs, a discriminant adaptive-weighted total variation model is introduced to optimize the intermediate reconstructed images. A fibrous phantom simulation and real experiment were performed to assess the performance of the proposed algorithm. Simulation and experimental results demonstrated that the proposed algorithm is an effective IL-PCCT reconstruction method for FBTs with incomplete projection data, and it has a great ability to suppress artifacts and preserve the edges of fibrous structures.