On-orbit space deployable antennas withstand periodic thermal loads, which will degrade the antenna surface accuracy. Thus, it is necessary to preliminarily adjust the antenna before launch to make it adapt to the space temperature environment as much as possible. Aiming at this problem, a pre-adjustment method based on min-max concept is presented in this study. First, according to the force equilibrium equation of the cable element, the incremental equilibrium equation of the cable mesh antenna is derived, and the incremental expressions of the reflector's surface displacement and cable tension with respect to cable length variation and element temperature variation are also developed. Then, the optimization model for shape pre-adjustment is established using min-max method, and the pre-adjustment process is implemented by sequence planning strategy. Finally, an AstroMesh antenna is employed to demonstrate the validity of the method.