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Hydraulic fracturing has been widely used in practical engineering as an essential means to prevent coal seam gas outburst, increase coal seam permeability and improve gas drainage efficiency. Accurate prediction of fracture propagation law is an important basis for optimizing fracturing parameters to achieve high-efficiency gas drainage in coal seams. In this paper, a new seepage–stress–damage coupling model considering permeability anisotropy is first established and then used to study the evolution laws of crack initiation pressure (σci), fracture pressure (σcd), AE behavior and pore water pressure with the lateral pressure coefficient (ξ) and permeability anisotropy coefficient (λ) in the process of hydraulic fracturing. Finally, the influence of initial pore water pressure on σci is discussed, and an efficient gas drainage method is proposed. Research results indicate that: the in situ stress still plays a leading role in the approach of crack propagation whether the permeability is isotropic or anisotropic; the non-uniform pressure condition is favorable for the crack growth compared with uniform pressure under the isotropic permeability condition; when the direction of maximum permeability is consistent with the direction of maximum principal stress (ξ = 0.5, λ < 0), the coal seams are easily fractured; AE behavior of fracturing holes can be divided into three stages: initiation stage, fracture smooth expansion stage and the breakdown stage for any λ or ξ; and the more complex the crack distribution, the more the area of the gas pressure release zone (GPRZ) increases, which is very beneficial to achieve high-efficiency gas drainage. This study can provide a basis for optimizing fracturing parameters and technology in improving the efficiency of coal seam gas drainage using the hydraulic fracturing method.