In this study, an efficient hybrid model is proposed to simulate the fluid flow in the reservoirs with multi-scale fractures, which cannot be easily modeled by neither the continuum models nor the discrete fracture models. In the proposed method, the small fractures are modeled by using an improved Multiple Sub-Region method, which can capture the strongly anisotropy of fracture elements and the effects of border region on the transmissibility and provide more accurate results, on the other hand, the large fractures are modeled explicitly as major fluid conduits by the Embedded Discrete Fracture Model. Then, an efficient numerical algorithm based on the Mimetic Finite Difference method is developed to solve the hybrid method. At the end, several numerical examples are carried out to verify the accuracy and applicability of the proposed numerical model.