In order to solve the problems of low efficiency of traditional filtered back projection reconstruction algorithm（FBP） and the noise, serious artifacts and blurred details of reconstructed image from incomplete projection when using CT to detect polymer-bonded explosives, sparse projection CT scanning method was chosen to improve detection efficiency. A prior image constrained compression sensing reconstruction algorithm was applied to suppress noise, reduce artifacts. A quasi-static uniaxial compression TATB-based PBX damage specimens was utilized to verify the CT scanning method and reconstruction algorithm. The FBP reconstruction results of the complete projection set, simultaneous algebra reconstruction technique (SART) and PICCS of sparse projection set were compared. The experimental results show that the reconstruction results of PICCS with 3 times sparse projection set are similar to that from the FBP reconstruction with the complete projection set, which can improve the detection efficiency by 2 times under the premise of satisfying the observation and judgment of the detected object defects and internal structure. Moreover, the reconstructed image of PICCS has fewer artifacts, smoother image and clearer details than SART reconstructed images.