An incomplete projection reconstruction algorithm was proposed in this study. In synchrotron radiation computed tomography (SRCT) of mechanical loading process, shielded projection due to the loading device is the main problem of high-resolution CT reconstruction. Thus, the proposed algorithm was developed based on information repairment considering the continuity of sinogram and slice. The truncated sinogram was estimated using orientation total variation minimization (TVM), which was based on the continuity of projections at adjacent angles in sinogram. Slice rectification was conducted to restrain image distortion, which was based on the continuity of matter contribution. Then, the algorithm was validated by a series of numerical reconstruction experiments. Results showed that the new algorithm could repair the lost boundary and restrain the artifacts. Quantitative comparison of evaluation parameters indicated that the new algorithm worked well when the shielded angle was less than 60 degrees and that satisfactory results could be obtained by approximately 200 times of iteration. Finally, the new algorithm was validated using actual SRCT data and demonstrated effective improvement of reconstruction quality. Therefore, the proposed algorithm may be a suitable method for the in situ SRCT studies of mechanical loading processes.