Projection-based embedded discrete fracture models (pEDFMs) are proven effective for modeling flow barrier effects of high-conductivity or impermeable fractures. However, local grid refinements are still needed to improve the accuracy of simulation in flow areas near fractures. In recent years, adaptive grid refinement techniques have received a lot of attention for dealing with highly heterogeneous and fractured models. But few of them are capable of EDFMs. In this paper, an adaptive grid refinement method under flow-based EDFMs (fEDFMs) is proposed for fractured models. The method starts from an fEDFM model which is built by a new technique of transmissibility modification by introducing an artificial pseudo-steady flow near fractures. Adaptive grid refinement and coarsening procedures are designed under an adaptive criterion based on both the fracture distribution and flow solutions. A flow-based upscaling procedure is adopted to form transmissibilities of the hybrid grids and the solution is mapped from the former grid system. The adaptive grid refinement method is applied in a validation case and a real field case, respectively. In each case, comparisons are made between the simulation results of the proposed adaptive grid refinement models and traditional uniform pEDFMs. Besides, comparisons are also made with the overall fine-scale models which serve as the reference models. The comparisons show that the numerical results of the proposed models have a better match to that of the reference models. And it is proven that the approach is more robust when applied to more general flow scenarios with extremely high or completely sealed fractures which could have a great impact on the flow. The proposed method aims to improve the accuracy of numerical simulation for fractured reservoirs.