Title: Learning Instance-Solution Operator For Optimal Control. Abstract: Optimal control problems (OCPs) aim at finding a control function for a dynamical system such that a cost functional is optimized. These problems are central to physical system research in both academia and industry. In this paper, we propose a novel instance-solution operator learning perspective, which solves OCPs in a one-shot manner with no dependence on the explicit expression of dynamics or iterative optimization processes. The design is in principle endowed with substantial speedup in running time, and the model reusability is guaranteed by high-quality in- and out-of-distribution generalization. We theoretically validate the perspective by presenting the approximation bounds for the instance-solution operator learning.  Extensive experiments on 6 physical systems verify the effectiveness and efficiency of our approach. The source code will be made publicly available.