Abstract: This paper is concerned with the design and guidance problems of a chaser satellite flyaround a target vehicle in non-coplanar elliptical orbit for a long time.At first,a(mathematical) model used to design a long-term flyaround trajectory is presented,which is(applicable) to the(situation) that a target spacecraft flies in an elliptical orbit.The conditions of the target at the center of the flyaround path are deduced.Considering the safety and task(requirement),a long-term(flyaround) trajectory is designed.Taking into account perturbations and navigation errors which can cause the trajectory unstable and mission impossible,a two-impulse control method is put forward.Some simulation works are carried out and the results indicate the flyaround mathematical model and the trajectory control method can be used in the design and control of a long-term flyaround trajectory.