To clarify the characteristics of fracture initiation in horizontal well in coal mine, a theoretical calculation model of fracture initiation in horizontal well in coal mine is established based on the regression equation of in-situ stress, the stress distribution of borehole wall and the maximum tensile stress criterion, and the influence of the depth and orientation of borehole on fracture initiation parameters is studied. The 3D discrete lattice numerical method is used to simulate the evolution of fracture initiation in horizontal well fracturing. The results show that the fracture initiation pressure of horizontal hole is influenced by the buried depth of formation and the azimuth of borehole. The fracture pressure is positively correlated with the buried depth. The buried depth increases from 150m to 1100m, and the peak fracture pressure increases by 46.47MPa. When the buried depth is less than 1100m, the fracture initiation pressure increases first and then decreases with the increase of the drilling azimuth. The borehole azimuth corresponding to the abrupt point of fracture initiation parameter decreases monotonically with the increase of burial depth. The crack initiation pressure reached its peak near the mutation point, and the crack initiation positions all changed from 90° to 0°. The fracture direction Angle suddenly increases from about 0° to a certain positive value, and then presents a parabolic change characteristic, and the fracture direction Angle is less than 27.08° within 1100m buried depth. The fracture initiation of borehole fracturing is a multi-stage evolution process, such as micro-fracture initiation, hole wall fracture line development and macroscopic fracture elliptic self-similar expansion. The research conclusion can provide reference for the optimization design of borehole layout scheme in underground coal mine.