Fluid flow modeling of coalbed methane (CBM) wells is effective in predicting gas production and designing appropriate depressurization schemes. Moreover, hydraulic fracturing is an important measure for improving the permeability of CBM reservoirs. In this work, we assumed the hydraulic fracture area near the main fracture to be rectangular. We developed a gas-water two-phase flow model considering the difference in stress sensitivity between the hydraulic fracturing area and the original coal reservoir. The numerical simulation results indicate that our model can accurately predict the production of CBM wells. In the early stage of CBM extraction, gas production increased with the increase of gas relative permeability. When the water saturation was below 0.7, the relative permeability of the gas phase was difficult to increase. At this time, the absolute permeability of the hydraulic fracturing area continued to decrease, leading to a decrease in gas production. Thus, if the difference of permeability evolution between the two areas is not considered, the production of CBM wells will be overestimated. In the process of CBM extraction, both reservoir pressure and water saturation decreased, but the distribution was inconsistent. The variation in reservoir pressure was mainly affected by absolute permeability and gas desorption, while the variation of water saturation was further affected by the distribution of relative permeability and initial water saturation. Therefore, the evolution of water saturation is generally more complex than that of reservoir pressure. In the hydraulic fracturing area, the effect of fracture compressibility on gas production was greater than the initial permeability. In the original coal reservoir, the larger initial permeability was more beneficial than the fracture compressibility for improving the production of CBM wells.