Carbonate reservoirs usually contain multi-scale fractures with a wide range of lengths and various levels of connectivities, which causes great challenges in reservoir simulation. To accurately characterize multi-scale fractures without dramatically increasing the number of simulation grids and computing time, a connectivity-based hierarchical model is proposed integrating different numerical models according to the geometrical size and fracture connectivity for different types of fractures. In this study, three types of fractures are defined. Large-scale fractures, which are usually characterized by seismic interpretations, are referred to as Type I fractures. They dominate the flow pattern globally due to their large geometrical and petrophysical properties. Thus, Type I fractures are modeled by discrete fracture model (DFM) in unstructured grids. For smaller fractures, we propose a methodology of fracture type classification to identify them as Type II and Type III fractures based on the level of connectivity to neighboring fractures. The resulting Type II fractures with relatively strong communications are characterized by a dual porosity/dual permeability model (DP). Type III fractures with weak communications contribute to an equivalent matrix system with enhanced porosity and permeability should be simulated by the enhanced matrix medium model (EMM). For integrating these three numerical models, the global flow-based upscaling method is applied to obtain transmissibilities. In order to test the accuracy and applicability, the proposed model is applied to a conceptual case of complicated fracture system and a field case of highly fractured carbonate reservoir in South China Sea, respectively. In the conceptual case, the simulation results of the proposed hierarchical model are compared with different classic models. The control group experiment demonstrates that the simulation results of the proposed hierarchical model are more accurate, compared to the classic models. A field case of four production wells are analyzed and discussed, which are drilled in the offshore carbonate reservoir with strong aquifer in South China Sea. Especially, water cuts increased rapidly within a short period in that reservoir. The simulation results show that our proposed model is capable of capturing such drastic flow accurately. As a result, the connectivity-based hierarchical model has great potential in characterizing multi-scale fracture system more precisely for reservoir simulation.