Explicit modeling of discrete fractures at the field scale is computationally intensive, and therefore, upscaling the fractures in the context of an equivalent continuum model is indispensable for field-scale simulations. This work introduces a new upscaling technique based on the local-global multiple-boundary (LG-MB) upscaling method for fluid flow in naturally fractured reservoirs. We extend the commonly-used local-global (LG) upscaling method by introducing a new approach to compute the fluid fluxes within the fractures crossing the grid-block boundaries. This method is based on the multiple-boundary (MB) approach applied within a local-global upscaling procedure. The global coarse-scale simulations are implemented to determine the boundary conditions for the calculations of local upscaled permeability. The procedure allows repeating the process to assure consistency between the global and local calculations. We implement the multi-point flux approximation (MPFA) finite volume method coupled with embedded discrete-fracture model within the MRST framework. We then verify the proposed LG-MB upscaling technique by comparing it with the reference fine-scale solutions and other existing local and local-global upscaling techniques. Results show that the proposed approach provides pronounced accuracy compared to local-based upscaled models with minor computational overhead. Compared to traditional local-global upscaling techniques, it provides more computational accuracy yet with the same efficiency. The superiority of the proposed LG-MB upscaling technique is attributed to two factors related to 1) the multiple-boundary technique to capture the flow behavior with high anisotropy from fractures non-alignment with the grid; 2) the use of local-global approach to accurately obtain the real flow boundary conditions. This work introduces a new upscaling method for flow simulation in naturally fractured reservoirs. We demonstrate its applicability in field applications and its superiority to existing upscaling methods. This method is accurate and straightforward and can be implemented within existing upscaling workflows.