With the development of shale-gas exploration and exploitation, it is necessary to study the 3D spatial distribution of shale fractures for research on shale rock physics. Because of limitations of instruments, accurate shale slice is discontinuous in depth, and the minimum interval between adjacent slices in depth is inconsistent with horizontal resolution of digital cores. Those are the main factors which can prevent accuracy improvement for fracture characterization and physical modeling of digital cores. In order to study the 3D spatial distribution of fractures, this abstract achieves reconstruction of 3D digital cores using Project Onto Convex Sets (POCS) method in curvelet domain. Tests on sand dataset obtained from X ray scanner and accurate shale rocks obtained by focused ion beam scanning electron microscopy (FIB-SEM) demonstrate the validity and superiority of the proposed method.