The cable-net structure of large peripheral truss deployable antenna is radiated by the sun and planets for a long period of time, resulting in large thermal deformation and mechanical relaxation, which degrades the service performance of the antenna. In this paper, an optimal control strategy for surface accuracy of shape memory cable-net (SMC) structure under space thermal radiation is proposed. First, the shape memory alloy (SMA) is introduced and integrated with the cable-net structure. The SMC structure with shape memory effect (SME) has the capability to transform the space thermal radiation into a favorable factor for on-orbit adjustment of surface accuracy, in order to realize the on-orbit shape preservation of cable-net antenna in space environment. Then, the space temperature field of cable-net structure is calculated. Finally, the cable-net structure with a diameter of 2 m is simulated, and the influence of the diameter of SMA wire, slope for the relation between the critical stress of phase transformation and inverse phase transformation and temperature on surface accuracy are analyzed. It shows that the implantation of SMA can greatly improve the surface accuracy of cable-net structure in a single thermal cycle.