<p>A novel equivalent negative stiffness viscous damping device (ENSVD) is proposed. This device provides a restoring force exclusively in the second and fourth quadrants of the force-displacement coordinate system. Consequently, it avoids increasing the maximum damping force of the isolation layer. In this paper, the steady-state response equation and equivalent linearization parameters of the ENSVD are derived using the slowly varying parameter method. Based on the shaking table scaled model of a high-rise shear wall structure, a combined analysis system of translational-swing base isolation with ENSVD is established, and its spectral characteristics are investigated using the complex modal method. The vibration control effect of the ENSVD on the rubber bearing isolation system is systematically evaluated based on far-field and near-field ground motion data. The results show that: the equivalent negative stiffness damping characteristics of the ENSVD can extend the structural period, significantly reduce the horizontal displacement of the isolation layer, and effectively prevent the amplification of the superstructure’s acceleration; meanwhile, its equivalent parameters are applicable to engineering analysis; compared with the viscous damper (VD) that provides restoring force in all four quadrants, the energy dissipation performance of the ENSVD is superior in short-period structures, while its displacement control effect on long-period structures is close to that of the VD; the VD will amplify the horizontal acceleration and isolation layer rotation angle of long-period structures, whereas the control effect of the ENSVD is more stable; the peak damping force of the ENSVD can effectively avoid the moment of the peak structural acceleration, which is beneficial to the control of structural acceleration.</p>