In-line X-ray phase-contrast computed tomography (IL-PCCT) is a valuable tool for revealing the internal detailed structures in weakly absorbing objects (e.g. biological soft tissues), and has a great potential to become clinically applicable. However, the long scanning time for IL-PCCT will result in a high radiation dose to biological samples, and thus impede the wider use of IL-PCCT in clinical and biomedical imaging. To alleviate this problem, a new iterative CT reconstruction algorithm is presented that aims to decrease the radiation dose by reducing the projection views, while maintaining the high quality of reconstructed images. The proposed algorithm combines the adaptive-weighted anisotropic total p-variation (AwaTpV, 0 < p < 1) regularization technique with projection onto convex sets (POCS) strategy. Noteworthy, the AwaTpV regularization term not only contains the horizontal and vertical image gradients but also adds the diagonal image gradients in order to enforce the directional continuity in the gradient domain. To evaluate the effectiveness and ability of the proposed algorithm, experiments with a numerical phantom and synchrotron IL-PCCT were performed, respectively. The results demonstrated that the proposed algorithm had the ability to significantly reduce the artefacts caused by insufficient data and effectively preserved the edge details under noise-free and noisy conditions, and thus could be used as an effective approach to decrease the radiation dose for IL-PCCT.