In this paper, a non-cooperation pursuit-evasion game universal framework of orbit-maneuver is proposed, to compensate for the degeneration in pursuit-evasion performance caused by delayed information from the ground decision-making to the orbital maneuver. History states of the spacecrafts serve as inputs for Informer, which works as a predictor to predict future states of the spacecrafts. With the predicted states as inputs, an online adaptive dynamic programming method is employed to solve the non-cooperation pursuit-evasion game problem to obtain an approximate optimal policy. Then, obtained results are fed back to Informer for further prediction. This process takes place in a rolling pattern. Moreover, stability analysis is conducted using the Lyapunov method, and the pursuit-evasion process is validated through simulation. Simulation results demonstrate the efficacy of the rolling prediction method in compensating for the performance degeneration.