An aeolian vibration model of transmission lines is designed and manufactured to grasp the vibration characteristics of large span overhead transmission lines. The vibration responses of a bare conductor and a conductor with a stockbridge damper are researched under different tension. The energy dissipation effect of the stockbridge damper and its installation position are analyzed and the results are compared with those of theoretical analysis. Then a calculating formula of damper installation position is proposed. The results show that the operation tension has a great impact on the aeolian vibration of large span conductors, and the controlling effect of the conductors' damping on aeolian vibration is very limited. The vibration amplitude of the conductor with a stock bridge damper is smaller than that of the bare conductor. However, with the increase of tension, the anti-vibration band of the damper gets narrowed and its anti-vibration effect reduces. The installation position of the damper has a great influence on the vibration of the conductor, and the vibration wave length at each excitation frequency should be considered when we determine the damper's installation position. The best anti-vibration band of FR-4 type stock bridge damper is from 15 to 25 Hz. For high frequency and low frequency vibration, its controlling effect is limited.