It is commonly believed that matrix and natural fractures randomly distribute in carbonate gas reservoirs. In order to increase the effective connected area to the storage space as much as possible, highly deviated wells are widely used for development. Although there have been some studies on the composite model for highly deviated wells, they have not considered the effects of stress sensitivity and threshold pressure gradient in a dual-porosity gas reservoir. In this paper, a semi-analytical composite model for low permeability carbonate gas reservoir was established to study the effect of non-Darcy flow. By employing source function, Fourier transform and the perturbation method, the pressure performance and typical well test curves were obtained. Eight flow regimes were identified, and their characteristics were discussed. As a result, it can be concluded that the effects of stress sensitivity and threshold pressure gradient would make pseudo-pressure and derivative curves rise, which is the characteristic of non-Darcy flow to determine whether there is stress sensitivity or threshold pressure gradient.