This paper proposes a differential game method with dynamic compensation, to solve the problem of space disturbance for spacecraft pursuit and escape. First, a pursuit and escaping game model of two disturbed spacecraft is established. Secondly, an extended state observer is designed to observe and compensate for the time-varying disturbance, transforming the game model to an approximate nominal model. The infinite-time optimal state regulator is used to solve the algebraic Riccati equation to obtain the optimal game strategy for the compensated approximate nominal model. Finally, the effectiveness of the proposed scheme is verified by simulation. The simulation results show that the dynamic compensation method can overcome the influence of disturbance, reduce the tracking error greatly, and improve the game task effect on both sides.