Tunnel construction in high geo-stress strata faces the risk of extreme natural disasters such as large squeezing deformation and rockburst. Therefore, it is of great significance to adopt a high-precision inversion method to investigate the distribution law of in situ stress in the tunnel site area. In this paper, the in situ stress inversion research was carried out based on a plateau tunnel with a buried depth of more than 1000 m. The idea of improving the inversion accuracy by unifying displacement constraints was proposed by aiming at the defects of the traditional method on the boundary conditions. Furthermore, the impact of the constant term in the regression model on the fitting accuracy was discussed. According to the inversion method with optimized fitting conditions, the in situ stress distribution characteristics in the tunnel site area were obtained, and the variation law of the in situ stress near the fault zone was discussed. The results showed that after unifying displacement constraints, the comprehensive inversion accuracy comprehensive indicator reflecting the inversion accuracy decreased from 15.291 to 12.895, indicating that the inversion error was effectively controlled. Whether the constant term should be retained had a random effect on the inversion accuracy, so it was recommended that this issue be independently verified when fitting the data. When approaching the inner side of the fault from the outer side, the in situ stress first increased slightly and then decreased significantly. Moreover, the wider the fault impact zone and the farther the fault distribution distance, the more significant the amplitude of stress change, e.g., the maximum amplitude of stress change reached 9.0 MPa. In addition, the in situ stress orientation near the fault can be significantly deflected. And the wider the fault impact zone, the more pronounced the deflection.