<p>In this paper, the issue of robust safety control for spacecraft proximity operations is investigated in the presence of model uncertainties and external disturbances. Initially, a line-of-sight-based relative dynamics model is established to describe the translational motion between the chaser spacecraft and the target spacecraft, based on this, a novel two-stage safety constraint including keep-out zone (Stage I) and field-of-view (FOV) corridor (Stage II) is introduced. Then, an adaptive model-based control scheme is proposed by exploiting the prescribed performance control approach. In addition, a neural networks-based model-free controller that relies only on the input/output measurement data is designed, which is more effective in the unknown and complex proximity process. It is shown that the derived controller can provide an online safety proximity trajectory for the chaser spacecraft while guaranteeing a prescribed convergence performance. Finally, simulations are given to verify the superiorities of the proposed method.</p>