With recovering oil prices, several shale gas resources may become economically viable for production. For efficient production of shale gas, it is important to understand complex mechanisms responsible for shale gas transport. It is driven by several flow mechanisms like Darcy flow, Knudsen diffusion and gas desorption, and is governed by highly non-linear flow equations. Conventionally, gas flow models have avoided non-linearity by ignoring hyperbolic term in diffusivity equation. However, flow equation is hyperbolic dominant for highly permeable fractures of shale and its significance should be analyzed. The mathematical model, depicting desorption-diffusion process under the isothermal condition, is presented for the gas transport mechanisms in shale. A transfer term is employed for coupling which characterizes the fluid transfer between matrix and fracture. The objective of this paper is to numerically model the pressure distribution in a dual porosity fractured shale reservoir due to the production of compressible gas. Equations are solved implicitly by finite volume method to give a stable solution. It shows that hyperbolic term is significant for initial pressure depletion period and its effect gradually diminishes with time. Hence hyperbolic flow term is significant, and considering it can improve performance prediction and enable efficient production of shale gas.