The permeability of coal seams is pore pressure-dependent. A number of analytical models have been proposed to investigate this problem, but many disregard a crucial factor: the anisotropy of coal. This paper is devoted to investigating the role of anisotropy in modeling the change of horizontal permeability with pressure. Analysis is conducted using a fully anisotropic model that incorporates both the anisotropies of mechanical properties and of the permeability dependence on stresses. Analytical expressions of the pressure-permeability relationship are derived in oedometric and isochoric geomechanical conditions, and validations are conducted against both laboratory and field data. Then, the roles of the anisotropy of stiffness and of permeability dependence on stresses in the permeability-change model are explored. We demonstrate that the mechanical anisotropy can be simplified to an isotropic model without introducing significant errors in prediction of pressure-permeability relationship, while neglecting the anisotropy of permeability dependence on stresses leads to considerable errors. When both anisotropy sources are disregarded, the pressure-permeability curve can be exactly reproduced by a totally isotropic material in both oedometric and isotropic conditions. However, the material properties (e.g., bulk modulus) are skewed; moreover, such an equivalent material might lead to significant errors in other geomechanical conditions. Finally, the permeability change is investigated at the reservoir scale, and the reservoir simulation results confirm the conclusions obtained from the analytical analysis.