Determining the dynamic synergistic deformation relationship of surrounding rock-support structure system is one of the key problems to be solved in underground engineering support. The synergistic equation of radial deformation of surrounding rock and radial deformation of supporting structure after tunnel excavation and support was derived by using Mohr-Coulomb criterion. The relationship between the plastic radius, displacement of surrounding rock and supporting stiffness of grade Ⅳ surrounding rock with supporting strength was discussed. FLAC^3D numerical simulation was used to verify the rationality and effectiveness of the synergistic deformation equation. The results show that the collaborative deformation equation of surrounding rock-supporting structure system can well reflect the relationship between surrounding rock displacement and plastic zone radius with the change of supporting strength, and the relationship is nonlinear. When the supporting strength is 0.75 MPa, the theoretical calculation of vault settlement is 18.9 mm, the numerical simulation of vault settlement is 21.6 mm. When the supporting strength is 1.5 MPa, the theoretical calculation of vault settlement is 11.2 mm, and the numerical simulation of vault settlement is 11.1 mm, which shows the effectiveness of the dynamic synergistic deformation equation of surrounding rock-supporting structure. In view of the Ⅳ surrounding rock in the use of advanced support and cross diaphragm (CRD) construction method, it is recommended that the support strength design is 0.75 ~ 1.5 MPa, the support stiffness design is 59.8 ~ 375.0 kN/mm.