Abstract: Aiming at a novel pinion rack type inertial viscous damper and, using the normalized complex-valued mode method, the performance parameters and energy-dissipation properties of the novel damper are discussed in detail. A shallow cable-inertial viscous damper vibration system is established. The normalized complex-valued mode method is used to derive the influence of the inertial coefficient and of the viscous coefficient on the cable’s modal damping ratio. The experimental and numerical investigations show that the displacement amplification effect caused by the negative stiffness makes the inertial viscous damper have a good damping effect on the cable. When considering the single-mode vibration, the inertial coefficient and the damping coefficient are different to achieve a higher single-mode damping ratio. When the inertial coefficient is an optimal value, the inertial viscous damper can simultaneously maximize the modal damping ratio of two adjacent vibration modes.