Propagation-based X-ray phase-contrast imaging (PBI) is a powerful nondestructive imaging technique that can reveal the internal detailed structures in weakly absorbing samples. Extending PBI to CT (PBCT) enables high-resolution and high-contrast 3D visualization of microvasculature, which can be used for the understanding, diagnosis and therapy of diseases involving vasculopathy, such as cardiovascular disease, stroke and tumor. However, the long scan time for PBCT impedes its wider use in biomedical and preclinical microvascular studies. To address this issue, a novel CT reconstruction algorithm for PBCT is presented that aims at shortening the scan time for microvascular samples by reducing the number of projections while maintaining the high quality of reconstructed images. The proposed algorithm combines the filtered backprojection method into the iterative reconstruction framework, and a weighted guided image filtering approach (WGIF) is utilized to optimize the intermediate reconstructed images. Notably, the homogeneity assumption on the microvasculature sample is adopted as prior knowledge, and therefore, a prior image of microvasculature structures can be acquired by a k-means clustering approach. Then, the prior image is used as the guided image in the WOLF procedure to effectively suppress streaking artifacts and preserve microvasculature structures. To evaluate the effectiveness and capability of the proposed algorithm, simulation experiments on 3D microvasculature numerical phantom and real experiments with CT reconstruction on the microvasculature sample are performed. The results demonstrate that the proposed algorithm can, under noise-free and noisy conditions, significantly reduce the artifacts and effectively preserve the microvasculature structures on the reconstructed images and thus enables it to be used for clear and accurate 3D visualization of microvasculature from few-projection data. Therefore, for 3D visualization of microvasculature, the proposed algorithm can be considered an effective approach for reducing the scan time required by PBCT. (C) 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement