A refined model of the shallow cable attached with two dampers（cable-two dampers） ， where one damper （damper Ⅰ） is a viscoelastic damper and the other one （damper Ⅱ） is a high damping rubber （HDR） damper， is established. General frequency formulas of the cable-two dampers system are then obtained. Two long cables of an existing cable-stayed bridge are used for experimental study and field monitoring. The long-term vibration monitoring of the cables with two dampers and with only one viscous-shear damper respectively has shown that the vortex-induced vibrations experienced by the cable only with the viscoelastic damper are successfully mitigated by the additional HDR damper. Besides， field tests on the cable damping before and after the installation of the HDR damper have indicated that the achievable damping ratios for the low-order modes of the cable are consistent with the corresponding theoretical estimates； meanwhile， the existence of the HDR damper somehow decreases the cable damping in low-order modes supplemented by the viscoelastic damper， and the reduction effect is more significant for the first several modes. Moreover， it is theoretically found that the stiffness of the viscoelastic damper helps improve the damping effect of the HDR damper on the high-order modes of the cable.