In this paper, based on the Hill-equation, the property of the flying-around orbit and the orbit design method of formation flying satellites are studied. The flying-around orbit is described in three respects: the coordinate-plane projection, the angle with the coordinate-plane, flying-around orbit elements. The orbit design of formation flying satellites is done in two steps: first the basic surrounding satellite, then the other surrounding satellites. Numerical results show that this method is suitable for the preliminary design of formation flying.