Whether the parabola can be close to an ideal parabolic surface has an important effect on the working efficiency of FAST. In this paper, the influence mechanism of radial expansion of FAST actuator on the shape adjustment of active reflector is analyzed, so as to explore the scheme to determine the ideal working face of FAST. Based on the geometric relations of paraboloids, an optimal model for determining the ideal paraboloid was established, and then euler transformation was carried out on the coordinate positions of the celestial bodies, and the hierarchical iterative algorithm was used to adjust the reflection surface, and the optimal model for adjusting the working paraboloid was established. Finally, the MATLAB was used to solve the model to determine the best working face position of FAST, and calculated that the reception efficiency of the feed cabin after adjustment has been improved by more than 90%. The optimization model established in this paper and the research results of layered iterative algorithm can be used as a reference for the working face adjustment of radio telescope in engineering application.