Long stay cables in cable-stayed bridges have low and close-spaced modal frequencies and are subjected to multimode vibrations, e.g., rain–wind vibrations and vortex-induced vibrations. Many types of dampers used in practice for cable vibration control can be described using a linear hysteretic damping model, e.g., high-damping rubber dampers and viscous-shear dampers. Such dampers are able to provide frequency-independent damping effects while the maximal achievable damping is limited due to their intrinsic stiffness effect. Therefore, this study investigates dampers with linear hysteretic damping enhanced by inerters for cable vibration control. A general inerter damper, consisting of a spring with complex stiffness and an inerter in parallel which is then connected to another inerter in series, is attached to a cable for dynamic analyses. Complex modal analysis is performed to appreciate cable damping. The optimal damping effect is discussed with reference to dynamic properties of the damper with respect to frequency, with comparison to the system of a cable with an inerter damper with viscous damping. It is found that two inerters, respectively in parallel and in series with a damper of linear hysteretic damping, can achieve a large improvement on multimode damping of a cable. The inertance of the inerter in series with the damper needs to be large for optimal performance while a small inertance of the other inerter is preferable. Furthermore, a case study based on a cable attached with a viscous-shear damper on the Sutong Bridge is conducted to show the feasibility of the inerter dampers. •Inerter dampers with linear hysteretic damping (IDHs) for cable vibration control.•Parametric studies on optimum multimode cable damping provided by an IDH.•IDHs compared with inerter dampers with viscous damping for cable vibration control.•A case study of using inerters in a cable–damper system of the Sutong Bridge.