The effective stress plays an essential role in predicting the permeability of the coal reservoir during coalbed methane (CBM) production. However, the importance of the effective stress coefficient (ESC) for permeability evolution has always been neglected. In this work, a series of permeability measurements were performed on cores of different directions under constant confining pressure (CCP) conditions and constant pore pressure conditions to demonstrate the different sensitivities of the anisotropic permeability on the confining stress and the pore pressure. Under CCP conditions, the loading and unloading results show that the irreversible permeability loss rate vertical to the bedding plane orientation is about 20% higher than that parallel to the horizon orientation. The in situ X-CT images indicate that the reason for irreversible permeability is that the microcleats cannot recover after the stress loading. The permeability variation with the increase of the Terzaghi effective stress presents an exponential law and a power law by changing the confining stress and changing the pore pressure for the same core, which suggests that the sensitivity of the permeability on the pore pressure is less than that on the confining stress. Then, the surface response method is used to calculate the ESC. The cores of different directions have different ESCs, ranging from 0.571 to 0.702. After correction of the ESC, the apparent permeability fits better with the effective stress. Finally, the role of the ESC in predicting the permeability during the CBM production is further investigated based on the S&D model. The modeling results indicate that the assumption of the effective stress coefficient as unity overestimates the increase of the effective stress during the reservoir pressure drawdown. The matrix shrinkage would dominate quickly for the lower effective stress coefficient. This study could be conducive to evaluate the stress sensitivity of coal reservoirs and predict the CBM production.