This paper presents the mission scenarios of using spinning tether system to conduct space stations fly-around mission and validates its feasibility. The main challenge of fly-around mission lies in the difficulty of balancing low fuel consumption and long-term fly-around observation. To deal with this problem, a novel spinning tether system is proposed. Firstly, the fly-around process with spinning tether system is introduced, and the tether system is modeled based on Newton-Euler method with a novel description of spinning motion. Secondly, Given the unique structural limitations of space stations, two fly-around schemes and referenced fly-around trajectories are detailed. Thirdly, a backstepping controller is proposed for tracking the reference motion of fly-around satellites, and the fuel consumption among different fly-around schemes is compared and analyzed. In the end, numerical results validate that under the proposed control strategy, the spinning tether system can maintain a stable fly-around configuration in both the planar and vertical plane, the symmetrical formation configuration prevents the central space station from being affected by the motion of fly-around satellites. Moreover, energy consumption analysis indicates that tethered system can save 62.8 % of impulse compared to traditional schemes when flying in the planar plane, making it the most energy-efficient option.