This paper emphasizes on the development of an improved mathematical model to understand the single-phase gas flow in a coupled matrix-fracture fluid mass exchange in a stress-sensitive reservoir along with the numerical investigations. Traditional methods for gas flow in fractured reservoirs don’t take into account the stress-sensitive fracture permeability. The focus of the present work is to study the highly nonlinear single-phase gas flow in a stress-sensitive fractured reservoir by using a dual-porosity model accompanied by the influence of quadratic gradient term in the fracture fluid flow equation. The results demonstrate that the stress-sensitivity of the fracture permeability negatively influences the pressure profiles and thus production. The pressure profile is underestimated when stress-sensitivity is not considered. The underestimation increases with increase in the pressure gradient and fracture permeability modulus. The underestimation is shown to vary from 106 Pa for constant pressure case to 105 Pa for constant rate case in the fracture. Additionally, higher fracture and matrix permeability results in an improved and homogeneous contribution throughout the rock-matrix. Thus, compared to the method used conventionally the present method can be employed to obtain more accurate pressure profiles and thus productivity of the reservoir. © 2020, © 2020 Taylor & Francis Group, LLC.