For the large spaceborne synthetic aperture radar antenna, its surface accuracy has a decisive impact on the on-orbit electrical performance, which is affected by manufacturing errors, assembly misalignments, and thermal deformations. Therefore, ensuring the surface accuracy on orbit and reducing its fluctuation are highly concerned issues for the large spaceborne antenna in practice. To this end, this study proposes an active adjustment method based on a multi-fidelity adaptive migration learning strategy to guarantee on-orbit surface accuracy. First, the theoretical surface accuracy model considering space thermal deformation is completely established. Then, the surrogate model of surface accuracy is developed to realize fast prediction and optimization, in which a new dynamic Kriging modeling method is proposed. Furthermore, the surrogate prediction model at other sites on the orbit is efficiently obtained by an innovative multi-fidelity migration learning strategy. On this basis, the active adjustment optimization model is constructed based on the surrogate prediction model, and the corresponding adjustment amounts can be obtained accordingly by solving this optimization problem. Finally, the effectiveness and advantages of the proposed method are comprehensively proven through case studies and experimental verification.