This paper proposes an adaptive neural network (NN) optimal control approach for autonomous relative motion control of non-cooperative spacecraft in proximity. The proposed method aims to minimize fuel consumption under various challenges including model uncertainty, state constraints, external disturbances, and input saturation. To account for uncertain parameters of non-cooperative target and external disturbances, we start by designing a NN disturbance observer. Subsequently, a novel optimal control index function is presented. An adaptive NN based on the actor-critic (A-C) framework and backstepping theory is then utilized to approximate the solution of Hamilton-Jacobi–Bellman (HJB) equation and obtain an optimal control law. The Lyapunov framework is leveraged to establish the stability of the closed-loop control system. Finally, numerical simulations are conducted to assess the feasibility and effectiveness of the proposed control scheme in comparison with an existing approach.