Predicting the initiation pressure of hydraulic fracturing is of great significance for oil and gas exploitation, in-situ stress measurement, and anti-cracking design of hydraulic structures. In this paper, the discontinuous numerical simulation method of particle discrete element combined with domain–pipe flow model is applied considering the fluid–solid coupling. Based on the front-advancing method, the granular model with a regular-shaped borehole is generated to analyze the meso cracking process and initiation pressure of hydraulic fracturing. According to the simulation results, the distribution of contact force chain on the borehole wall is consistent with the theoretical solution on the basis of eliminating the irregularity of borehole shape. The fitted initiation pressure formula by DEM is also close to the theoretical solution. Furthermore, the difference between the fitting formula of initiation pressure and the theoretical solution is explained from the perspective of the local tensile force generated when the granular material is compressed. Finally, a method for preparing impermeable mortar samples with prefabricated boreholes is designed. The initiation pressure under different principal stresses is quantitatively studied based on the true triaxial laboratory tests, which verifies the reliability of the discrete element simulation results.