Orbital pursuit-evasion, as a research hotspot in the field of aerospace dynamics and control, has garnered increasing attention from a growing number of researchers. The paper addresses the issue of constructing the closed-loop equilibrium for close-range orbital pursuit-evasion games and proposes a computation method that integrates Bellman’s Principle of Optimality, the finite difference method, and interpolation techniques. A dimension-reduction dynamics of the game system in the line-of-sight coordinate frame is derived, establishing a close-range orbital pursuit-evasion game model and reducing the dimensionality of the system’s state space. Based on Bellman’s Principle of Optimality, the original problem is reformulated as a Hamilton-Jacobi-Isaacs (HJI) Partial Differential Equation (PDE) terminal value problem, enabling the simultaneous handling of multiple game scenarios through reverse-time analysis. The state space is discretized using Cartesian grids, and the finite difference method is employed to calculate the dynamic evolution process of the equilibrium driven by the dynamics, and analyze the game situation. Utilizing the relationship between control and the spatial gradient of the equilibrium, numerical interpolation is applied to construct the closed-loop control function. The effectiveness of the proposed method is demonstrated through numerical simulations.