Characterzied with its common unfavorable geological structure in tunnel construction, fault fracture zone often brings about instability or even collapse of surrounding rock during construction near the fault fracture zone. In view of a study of its impact on the stability of tunnel surrounding rock and support structure, a three-dimensional analysis model has thus been established using FLAC3D based on a certain highway tunnel. The calculation results indicate that under the three construction methods, the settlement value of the arch top and the uplift value of the arch bottom of the surrounding rock at the location of the fault fracture zone are significantly greater than those in the normal section of the surrounding rock. Meanwhile, the initial support structure bears the maximum force at the junction of the fault fracture zone and the normal section of the surrounding rock. The maximum vault settlement value of the arch crown caused by the construction of the reserved core geotechnical method for annular excavation is 51.45 mm, the maximum uplift value of arch bottom is 121.25 mm, and the maximum principal stress of the initial support structure is 15.27 MPa. All data are superior to the other two construction methods, indicating that this proposed method achieves the best effect on maintaining the stability of surrounding rock. It is suggested that the monitoring and measurement be strengthened of the location of fault fracture zones during on-site construction, with further safety measures to be taken.