The stress sensitivity of abnormally pressured carbonate gas reservoirs is of great complexity and exerts much influence on gas well deliverability calculation. Fifty core samples from the AD Gas Reservoirs were selected in the experiment to study the effect of abnormally high pressure and fracture on the stress sensitivity of carbonate gas reservoir. The results show that the permeability decline mainly occurs in the abnormally high-pressure stage and is rather small in normal pressure stage. The existence of the fracture could substantially enhance the stress sensitivity. The higher fracture density could induce the stronger stress sensitivity. Furthermore, a mathematical model with the consideration of the variable permeability modulus was established to calculate gas well deliverability in the abnormally pressured carbonate gas reservoir with developed natural fractures. It is revealed that previous method assuming a fixed permeability modulus would lead to an overestimation of the real stress sensitivity and thus underestimating the absolute open flow of the gas well.