At present, many high gas and outburst mines have poor gas drainage effects. An important reason influencing the gas drainage effect is a poor hole-sealing effect. Most studies on gas drainage borehole sealing focus on local and foreign borehole sealing methods, borehole sealing equipment, and borehole sealing materials. Numerical simulations of initial drilling sealing depth are insufficient because studies on this subject are few. However, when the initial sealing depth of the borehole is not chosen reasonably, air can enter the gas drainage drill hole through the circumferential crack of roadway surrounding rocks under the influence of suction pressure of the drainage system. This phenomenon ultimately affects the hole-sealing effect. To improve the drilling hole sealing of gas drainage boring, we deduced the expression formulas of the crushing zone, plastic zone, and elastic zone around the coal-seam floor stone drift and conducted a stress–strain analysis of the coal-seam floor stone drift of the 2145 working surfaces of the Sixth Coal Mine of Hebi Coal Mine Group Company by using theoretical analysis, numerical simulation, and on-scene verification. Finally, we obtain the initial drilling sealing depth, which is a main contribution of this study. The results prove the following. The performed hole-sealing process with an initial drilling sealing depth of 8 m has a gas drainage efficiency of 55%. Compared with the previous 6.8 m initial drilling sealing depth with a gas drainage efficiency of less than 30%, which was adopted by the mine, the initial sealing depth of 8 m chosen in the numerical simulation is reasonable and conforms to the actual situation on the spot. Therefore, the initial drilling sealing depth chosen in the numerical simulation will produce practical and effective guidance to study the field hole-sealing depth.