In this paper a Cryogenic Giant Magnetostrictive Materials (CGMM) actuator using HTS was designed, taking into account both the coupled field characteristics of the CGMM and the anisotropy of the investigated Bi2223/Ag HTS tapes. Then an optimal structure, which costs the least HTS tapes while still make the CGMM to the state of saturation, is realized by combining the genetic algorithm (GA) with the coupled field iteration of FEM.