Abstract: Characterizing pore structure of shale is the basic work for shale reservoir evaluation. Shale in this study is collected from the upper Triassic Yanchang formation in Ordos Basin. Pore structures including pores and throats, in spaces 10 μm³, 20 μm³, 30 μm³, 39 μm³, are investigated with Nano-CT(scanning accuracy is 65 nm). The numbers of pores and throats connecting with pores in different spaces are counted. Assuming pores and throats as balls and tubes, respectively, the physical models "ball-and -tube models" of pore structures are abstracted. The corresponding mathematical models of pore connectivity are founded through complex network theory. The pores and throats are respectively treated as nodes and edges. The pore connectivity network in 10 μm³ is constructed by Matlab software according to the mathematical characterizes of scale-free network. The conception of network connectivity entropy is introduced to assess the heterogeneity of pore connectivity networks. The investigation indicates that the pore connectivity networks in spaces 10 μm³, 20 μm³ and 39 μm³ are the scale free networks whose degree distribution conforms to power law distribution. The degree distribution of pore connectivity networks in spaces 10 μm³ accords with exponential distribution. The connectivity of pore and throat network decreases as the network connectivity entropy increases. The method in this study can be used to evaluate the connectivity of porous structures of shale, and assess the porous and permeable characteristics of shale gas reservoir.