In order to find out the influence of abnormal high pressure on gas well productivity in carbonate gas reservoirs, based on three types of reservoirs in Qixia Formation of Anyue gas field, the influence of three types of reservoirs on gas well productivity under abnormal high pressure is quantitatively described according to stress sensitivity experimental analysis, gas well productivity change characteristics and numerical simulation research results. The results show that (1) through the stress sensitivity experiment, it is found that the stress sensitivity intensity of three types of reservoirs is fractured-vuggy type, vuggy type and porous type in turn; (2) When formation pressure drops to abandonment pressure, the decrease rate of open flow of gas wells in fractured-vuggy reservoirs, vuggy reservoirs and porous reservoirs with stress sensitivity is 14.90, 8.56 and 6.04% faster than that without stress sensitivity, respectively; (3) Numerical simulation shows that the average recovery degree of three types of reservoirs is reduced by 7.23% when considering the stress sensitivity of reservoirs. The main contribution of gas well productivity comes from vuggy type, fractured-vuggy type and porous type reservoirs in turn, and the contribution of productivity per unit reservoir thickness is fractured-vuggy type, vuggy and porous type reservoirs in turn, and its contribution order will not change due to reservoir stress sensitivity. The research results show that fracture-cavity and cavity reservoirs have strong stress sensitivity and great influence on gas well productivity, but they are still relatively high-quality reservoirs. This achievement provides technical support for the benefit development of Qixia formation gas reservoir, and can provide reference for the productivity research of gas wells in similar gas reservoirs.