The issue of constructing the closed-loop equilibrium for close-range orbital pursuit-evasion games was addressed and a computation method that integrates Bellman′s principle of optimality, the finite difference method, and interpolation techniques was proposed. A dimension-reduction dynamics of the game system in the line-of-sight coordinate frame was derived, establishing a close-range orbital pursuit-evasion game model and reducing the dimensionality of the systems state space. Based on Bellman′s principle of optimality, the original problem was reformulated as a Hamilton-Jacobi-Isaacs partial differential equation terminal value problem, enabling the simultaneous handling of multiple game scenarios through reverse-time analysis. The state space was discretized using Cartesian grids, and the finite difference method was 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 was applied to construct the closed-loop control function. The effectiveness of the proposed method was demonstrated through numerical simulations.