The structure of the railway catenary determines the current collection quality of the pantograph-catenary system. As the catenary is a tension structure with small damping, it takes several minutes to back to the static state once it vibrates. Due to the wave propagations, the contact wire starts to vibrate before a front pantograph reaches, and a rear pantograph faces a worse condition. To lighten the catenary’s earlier vibration, a damping-enhanced catenary structure with unidirectional rotary dampers is proposed. The unidirectional rotary dampers are adopted and installed on the supporting of the steady arms, making which to be undamped for the uplift process and damped for the falling process. The enhanced damping values can be acquired through experiments. The dynamics of the proposed structure are studied and compared with the traditional one. The results show that it’s an effective way to alleviate the catenary’s vibration and improve contact quality, especially for a rear pantograph, which may be promising for the 400 km/h or higher speed railway.