Porosity and permeability plays an important role in the investigation of the flow ability of unconventional rock. Unconventional rock such as shale gas has extremely low permeability due to nano-scale pores. Non-Darcy flow typically applies to any inertial flow where the Reynolds number is higher than 1. The study of non-Darcy flow in porous rocks by experiments carried out in the laboratory is consistently characterized by high costs and time-consuming procedures. In this study, a novel method called the lattice Boltzmann method, an alternative to the laboratory method has been used for the study of non-Darcy flow of shale gas. It provides matrix permeability from pore structure considering inertial flow which causes departure from Darcy’s law. The characteristics of non-Darcy flow are significantly influenced by the pore structure of a porous medium, with a more heterogeneous structure such as in the case of shale exhibiting a more rapid termination of Darcy flow. Two samples of shale as large as 5 mm of southern Karanpura were taken for this study. Computed micro-tomography images were acquired at 0.4 μm and 0.8 μm. The study of non-Darcy fluid flow in shale gas showed that as velocity increases, an inertial effect gets dominated in flow which results in a lowering of permeability. Earlier onset of non-Darcy behavior in complex structures is also investigated. Developing a complete understanding of the transport properties and developing an approach to assess the prospective gas flow is essential in informing the estimation of shale gas reserves and developing effective recovery strategies.