To meet the computational requirements of safe airspace and the expected landing point in the recovery mission of the reentry capsule, a fast prediction algorithm of the flight pipeline based on the Koopman operator approach was proposed for the reentry capsule and the determination process for safe flight airspace of search and rescue helicopters was provided. The body-parachute dynamic model was constructed. A group of discrete state points was uniformly selected from the random state space by using the Halton sampling method, and the multiple possible trajectory was calculated. Based on the back pulling mechanism of Koopman operator, the initial probability density value was associated with the current state to obtain the flight pipeline and desired trajectory of the reentry capsule and its separation parts under uncertain conditions.The simulation results show that the fast prediction algorithm of the flight pipeline based on the Koopman operator approach is significantly better than the Monte Carlo method in terms of convergence speed and accuracy. After using the flight pipeline calculation results to plan the flight route of the rescue helicopter, the collision risk is reduced by 54% at most and the corresponding search time is reduced by 70%. The proposed algorithm has been successfully applied to the Chang′e-5 recovery mission.