China is now building the largest single dish radio telescope in the world in Guizhou province, which is called Five-hundred meter Aperture Spherical radio Telescope (FAST). A Stewart platform is introduced in FAST as an accuracy adjustable mechanism for feed receivers. The main purpose of this paper is to discuss dimension optimization design method of the Stewart platform based on three optimization objective functions. The optimization objective functions can reflect the operability and accuracy of the Stewart platform, and optimization design flow is presented according to the important degree of the three optimization objectives. Finally, a set of optimized parameters is obtained, and the study in this paper provides a basis for the coming optimization the feed support system for FAST in the next step.